Results of Incomplete Gamma and Related Functions: Difference between revisions

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Notation: 8.1 Special Notation
Incomplete Gamma Functions: 8.2 Definitions and Basic Properties
8.3 Graphics
8.4 Special Values
8.5 Confluent Hypergeometric Representations
8.6 Integral Representations
8.7 Series Expansions
8.8 Recurrence Relations and Derivatives
8.9 Continued Fractions
8.10 Inequalities
8.11 Asymptotic Approximations and Expansions
8.12 Uniform Asymptotic Expansions for Large Parameter
8.13 Zeros
8.14 Integrals
8.15 Sums
8.16 Generalizations
Related Functions: 8.17 Incomplete Beta Functions
8.18 Asymptotic Expansions of Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normincBetaI{x}@{a}{b}}
8.19 Generalized Exponential Integral
8.20 Asymptotic Expansions of Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genexpintE{p}@{z}}
8.21 Generalized Sine and Cosine Integrals
Applications: 8.22 Mathematical Applications
8.23 Statistical Applications
8.24 Physical Applications
Computation: 8.25 Methods of Computation
8.26 Tables
8.27 Approximations
8.28 Software

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+<div style="-moz-column-count:2; column-count:2;">
-{| class="wikitable sortable" style="margin: 0;"
+; Notation : [[8.1|8.1 Special Notation]]<br>
-|-
+; Incomplete Gamma Functions : [[8.2|8.2 Definitions and Basic Properties]]<br>[[8.3|8.3 Graphics]]<br>[[8.4|8.4 Special Values]]<br>[[8.5|8.5 Confluent Hypergeometric Representations]]<br>[[8.6|8.6 Integral Representations]]<br>[[8.7|8.7 Series Expansions]]<br>[[8.8|8.8 Recurrence Relations and Derivatives]]<br>[[8.9|8.9 Continued Fractions]]<br>[[8.10|8.10 Inequalities]]<br>[[8.11|8.11 Asymptotic Approximations and Expansions]]<br>[[8.12|8.12 Uniform Asymptotic Expansions for Large Parameter]]<br>[[8.13|8.13 Zeros]]<br>[[8.14|8.14 Integrals]]<br>[[8.15|8.15 Sums]]<br>[[8.16|8.16 Generalizations]]<br>
-! scope="col" style="position: sticky; top: 0;" | DLMF
+; Related Functions : [[8.17|8.17 Incomplete Beta Functions]]<br>[[8.18|8.18 Asymptotic Expansions of <math>\normincBetaI{x}@{a}{b}</math>]]<br>[[8.19|8.19 Generalized Exponential Integral]]<br>[[8.20|8.20 Asymptotic Expansions of <math>\genexpintE{p}@{z}</math>]]<br>[[8.21|8.21 Generalized Sine and Cosine Integrals]]<br>
-! scope="col" style="position: sticky; top: 0;" | Formula
+; Applications : [[8.22|8.22 Mathematical Applications]]<br>[[8.23|8.23 Statistical Applications]]<br>[[8.24|8.24 Physical Applications]]<br>
-! scope="col" style="position: sticky; top: 0;" | Constraints
+; Computation : [[8.25|8.25 Methods of Computation]]<br>[[8.26|8.26 Tables]]<br>[[8.27|8.27 Approximations]]<br>[[8.28|8.28 Software]]<br>
-! scope="col" style="position: sticky; top: 0;" | Maple
-! scope="col" style="position: sticky; top: 0;" | Mathematica
-! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
-! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
-! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
-! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
-|-
-|-
-| [https://dlmf.nist.gov/8.2.E1 8.2.E1] || [[Item:Q2480|<math>\incgamma@{a}{z} = \int_{0}^{z}t^{a-1}e^{-t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = \int_{0}^{z}t^{a-1}e^{-t}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = int((t)^(a - 1)* exp(- t), t = 0..z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == Integrate[(t)^(a - 1)* Exp[- t], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 21] || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.2.E2 8.2.E2] || [[Item:Q2481|<math>\incGamma@{a}{z} = \int_{z}^{\infty}t^{a-1}e^{-t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = \int_{z}^{\infty}t^{a-1}e^{-t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = int((t)^(a - 1)* exp(- t), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Integrate[(t)^(a - 1)* Exp[- t], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 42]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = -2, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = -2, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 42]
-|-
-| [https://dlmf.nist.gov/8.2.E3 8.2.E3] || [[Item:Q2482|<math>\incgamma@{a}{z}+\incGamma@{a}{z} = \EulerGamma@{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z}+\incGamma@{a}{z} = \EulerGamma@{a}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z)+ GAMMA(a, z) = GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z]+ Gamma[a, z] == Gamma[a]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.2#Ex1 8.2#Ex1] || [[Item:Q2483|<math>\normincGammaP@{a}{z} = \frac{\incgamma@{a}{z}}{\EulerGamma@{a}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a}{z} = \frac{\incgamma@{a}{z}}{\EulerGamma@{a}}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = (GAMMA(a)-GAMMA(a, z))/(GAMMA(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, 0, z] == Divide[Gamma[a, 0, z],Gamma[a]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.2#Ex2 8.2#Ex2] || [[Item:Q2484|<math>\normincGammaQ@{a}{z} = \frac{\incGamma@{a}{z}}{\EulerGamma@{a}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaQ@{a}{z} = \frac{\incGamma@{a}{z}}{\EulerGamma@{a}}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z)/GAMMA(a) = (GAMMA(a, z))/(GAMMA(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, z] == Divide[Gamma[a, z],Gamma[a]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.2.E5 8.2.E5] || [[Item:Q2485|<math>\normincGammaP@{a}{z}+\normincGammaQ@{a}{z} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a}{z}+\normincGammaQ@{a}{z} = 1</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(a)-GAMMA(a, z))/GAMMA(a)+ GAMMA(a, z)/GAMMA(a) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, 0, z]+ GammaRegularized[a, z] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.2.E6 8.2.E6] || [[Item:Q2486|<math>\scincgamma@{a}{z} = z^{-a}\normincGammaP@{a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scincgamma@{a}{z} = z^{-a}\normincGammaP@{a}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = (z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || Skip - symbolical successful subtest || -
-|-
-| [https://dlmf.nist.gov/8.2.E6 8.2.E6] || [[Item:Q2486|<math>z^{-a}\normincGammaP@{a}{z} = \frac{z^{-a}}{\EulerGamma@{a}}\incgamma@{a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{-a}\normincGammaP@{a}{z} = \frac{z^{-a}}{\EulerGamma@{a}}\incgamma@{a}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a) = ((z)^(- a))/(GAMMA(a))*GAMMA(a)-GAMMA(a, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(z)^(- a)* GammaRegularized[a, 0, z] == Divide[(z)^(- a),Gamma[a]]*Gamma[a, 0, z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2669922311+.3869142026*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.493684189-.9843316111*I
-Test Values: {a = 1.5, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.2.E7 8.2.E7] || [[Item:Q2487|<math>\scincgamma@{a}{z} = \frac{1}{\EulerGamma@{a}}\int_{0}^{1}t^{a-1}e^{-zt}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scincgamma@{a}{z} = \frac{1}{\EulerGamma@{a}}\int_{0}^{1}t^{a-1}e^{-zt}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = (1)/(GAMMA(a))*int((t)^(a - 1)* exp(- z*t), t = 0..1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Successful [Tested: 21] || -
-|-
-| [https://dlmf.nist.gov/8.2.E8 8.2.E8] || [[Item:Q2488|<math>\incgamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incgamma@{a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incgamma@{a}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z*exp(2*Pi*m*I)) = exp(2*Pi*m*I*a)*GAMMA(a)-GAMMA(a, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z*Exp[2*Pi*m*I]] == Exp[2*Pi*m*I*a]*Gamma[a, 0, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [28 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.772453851+.14e-8*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, m = 1, a = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.772453851+.62e-8*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, m = 3, a = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.2.E9 8.2.E9] || [[Item:Q2489|<math>\incGamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incGamma@{a}{z}+(1-e^{2\pi mia})\EulerGamma@{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incGamma@{a}{z}+(1-e^{2\pi mia})\EulerGamma@{a}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z*exp(2*Pi*m*I)) = exp(2*Pi*m*I*a)*GAMMA(a, z)+(1 - exp(2*Pi*m*I*a))*GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z*Exp[2*Pi*m*I]] == Exp[2*Pi*m*I*a]*Gamma[a, z]+(1 - Exp[2*Pi*m*I*a])*Gamma[a]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [28 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.701776495-.3980325655*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.701776493-.3980325669*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, m = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [28 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.7017764946044596, -0.3980325648566406]
-Test Values: {Rule[a, 1.5], Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.7017764946044598, -0.39803256485664035]
-Test Values: {Rule[a, 1.5], Rule[m, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.2.E10 8.2.E10] || [[Item:Q2490|<math>e^{-\pi ia}\incGamma@{a}{ze^{\pi i}}-e^{\pi ia}\incGamma@{a}{ze^{-\pi i}} = -\frac{2\pi i}{\EulerGamma@{1-a}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-\pi ia}\incGamma@{a}{ze^{\pi i}}-e^{\pi ia}\incGamma@{a}{ze^{-\pi i}} = -\frac{2\pi i}{\EulerGamma@{1-a}}</syntaxhighlight> || <math>\realpart@@{(1-a)} > 0</math> || <syntaxhighlight lang=mathematica>exp(- Pi*I*a)*GAMMA(a, z*exp(Pi*I))- exp(Pi*I*a)*GAMMA(a, z*exp(- Pi*I)) = -(2*Pi*I)/(GAMMA(1 - a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- Pi*I*a]*Gamma[a, z*Exp[Pi*I]]- Exp[Pi*I*a]*Gamma[a, z*Exp[- Pi*I]] == -Divide[2*Pi*I,Gamma[1 - a]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [28 / 28]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.710645106+2.690107924*I
-Test Values: {a = -1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1295806364+5.171352915*I
-Test Values: {a = -1.5, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [28 / 28]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.710645107283499, 2.690107923521634]
-Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.12958063668571548, 5.171352913200156]
-Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || [[Item:Q2491|<math>\incGamma@{a}{ze^{+\pi i}} = \EulerGamma@{a}(1-z^{a}e^{+\pi ia}\scincgamma@{a}{-z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{ze^{+\pi i}} = \EulerGamma@{a}(1-z^{a}e^{+\pi ia}\scincgamma@{a}{-z})</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z*exp(+ Pi*I)) = GAMMA(a)*(1 - (z)^(a)* exp(+ Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [4 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.046852240-1.006153525*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4563214597+.8560373719*I
-Test Values: {a = 1.5, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
-|-
-| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || [[Item:Q2491|<math>\incGamma@{a}{ze^{-\pi i}} = \EulerGamma@{a}(1-z^{a}e^{-\pi ia}\scincgamma@{a}{-z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{ze^{-\pi i}} = \EulerGamma@{a}(1-z^{a}e^{-\pi ia}\scincgamma@{a}{-z})</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z*exp(- Pi*I)) = GAMMA(a)*(1 - (z)^(a)* exp(- Pi*I*a)*(- z)^(-(a))*(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.510498964-.9249588863*I
-Test Values: {a = 1.5, z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7017764949-.3980325647*I
-Test Values: {a = 1.5, z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
-|-
-| [https://dlmf.nist.gov/8.2.E12 8.2.E12] || [[Item:Q2492|<math>\deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])+(1 +(1 - a)/(z))*diff(w, z) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+(1 +Divide[1 - a,z])*D[w, z] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
-|-
-| [https://dlmf.nist.gov/8.2.E13 8.2.E13] || [[Item:Q2493|<math>\deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(2)])-(1 +(1 - a)/(z))*diff(w, z)+(1 - a)/((z)^(2))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]-(1 +Divide[1 - a,z])*D[w, z]+Divide[1 - a,(z)^(2)]*w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.165063509-1.250000000*I
-Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.165063509+1.250000000*I
-Test Values: {a = -1.5, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.1650635094610964, -1.25]
-Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.1650635094610964, 1.2500000000000004]
-Test Values: {Rule[a, -1.5], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E1 8.4.E1] || [[Item:Q2495|<math>\incgamma@{\tfrac{1}{2}}{z^{2}} = 2\int_{0}^{z}e^{-t^{2}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{\tfrac{1}{2}}{z^{2}} = 2\int_{0}^{z}e^{-t^{2}}\diff{t}</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2)) = 2*int(exp(- (t)^(2)), t = 0..z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[Divide[1,2], 0, (z)^(2)] == 2*Integrate[Exp[- (t)^(2)], {t, 0, z}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.465949776-3.038201708*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.197911286+.8974462698*I
-Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[3.4659497742269214, -3.038201707267986]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.197911285535813, 0.8974462701863266]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E1 8.4.E1] || [[Item:Q2495|<math>2\int_{0}^{z}e^{-t^{2}}\diff{t} = \sqrt{\pi}\erf@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\int_{0}^{z}e^{-t^{2}}\diff{t} = \sqrt{\pi}\erf@{z}</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>2*int(exp(- (t)^(2)), t = 0..z) = sqrt(Pi)*erf(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*Integrate[Exp[- (t)^(2)], {t, 0, z}, GenerateConditions->None] == Sqrt[Pi]*Erf[z]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.4.E2 8.4.E2] || [[Item:Q2496|<math>\scincgamma@{a}{0} = \frac{1}{\EulerGamma@{a+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scincgamma@{a}{0} = \frac{1}{\EulerGamma@{a+1}}</syntaxhighlight> || <math>\realpart@@{(a+1)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(0)^(-(a))*(GAMMA(a)-GAMMA(a, 0))/GAMMA(a) = (1)/(GAMMA(a + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7522527782
-Test Values: {a = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.128379167
-Test Values: {a = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
-|-
-| [https://dlmf.nist.gov/8.4.E3 8.4.E3] || [[Item:Q2497|<math>\scincgamma@{\tfrac{1}{2}}{-z^{2}} = \frac{2e^{z^{2}}}{z\sqrt{\pi}}\DawsonsintF@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scincgamma@{\tfrac{1}{2}}{-z^{2}} = \frac{2e^{z^{2}}}{z\sqrt{\pi}}\DawsonsintF@{z}</syntaxhighlight> || <math>\realpart@@{(\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>(- (z)^(2))^(-((1)/(2)))*(GAMMA((1)/(2))-GAMMA((1)/(2), - (z)^(2)))/GAMMA((1)/(2)) = (2*exp((z)^(2)))/(z*sqrt(Pi))*dawson(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
-|-
-| [https://dlmf.nist.gov/8.4.E4 8.4.E4] || [[Item:Q2498|<math>\incGamma@{0}{z} = \int_{z}^{\infty}t^{-1}e^{-t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{0}{z} = \int_{z}^{\infty}t^{-1}e^{-t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(0, z) = int((t)^(- 1)* exp(- t), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[0, z] == Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.4.E4 8.4.E4] || [[Item:Q2498|<math>\int_{z}^{\infty}t^{-1}e^{-t}\diff{t} = \expintE@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{z}^{\infty}t^{-1}e^{-t}\diff{t} = \expintE@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int((t)^(- 1)* exp(- t), t = z..infinity) = Ei(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(- 1)* Exp[- t], {t, z, Infinity}, GenerateConditions->None] == ExpIntegralE[1, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.393548628-1.498247032*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8944744989-3.773814377*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.4.E5 8.4.E5] || [[Item:Q2499|<math>\incGamma@{1}{z} = e^{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{1}{z} = e^{-z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(1, z) = exp(- z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[1, z] == Exp[- z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.4.E6 8.4.E6] || [[Item:Q2500|<math>\incGamma@{\tfrac{1}{2}}{z^{2}} = 2\int_{z}^{\infty}e^{-t^{2}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{\tfrac{1}{2}}{z^{2}} = 2\int_{z}^{\infty}e^{-t^{2}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA((1)/(2), (z)^(2)) = 2*int(exp(- (t)^(2)), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[Divide[1,2], (z)^(2)] == 2*Integrate[Exp[- (t)^(2)], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.465949776+3.038201708*I
-Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.197911286-.8974462698*I
-Test Values: {z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-3.4659497742269214, 3.038201707267986]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-3.1979112855358127, -0.8974462701863266]
-Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E6 8.4.E6] || [[Item:Q2500|<math>2\int_{z}^{\infty}e^{-t^{2}}\diff{t} = \sqrt{\pi}\erfc@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>2\int_{z}^{\infty}e^{-t^{2}}\diff{t} = \sqrt{\pi}\erfc@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>2*int(exp(- (t)^(2)), t = z..infinity) = sqrt(Pi)*erfc(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>2*Integrate[Exp[- (t)^(2)], {t, z, Infinity}, GenerateConditions->None] == Sqrt[Pi]*Erfc[z]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.4.E7 8.4.E7] || [[Item:Q2501|<math>\incgamma@{n+1}{z} = n!(1-e^{-z}e_{n}(z))</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{n+1}{z} = n!(1-e^{-z}e_{n}(z))</syntaxhighlight> || <math>\realpart@@{(n+1)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(n + 1)-GAMMA(n + 1, z) = factorial(n)*(1 - exp(- z)*exp(1)[n]*(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[n + 1, 0, z] == (n)!*(1 - Exp[- z]*Subscript[E, n]*(z))</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.7896317094254578, 0.19173078621885742], Times[Complex[0.42050290937849244, 0.009925196319850484], Subscript[2.718281828459045, 1]]]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.06153297742196945, 0.16461464559793018], Times[-2.0, Plus[1.0, Times[Complex[-0.42050290937849244, -0.009925196319850484], Subscript[2.718281828459045, 2]]]]]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E8 8.4.E8] || [[Item:Q2502|<math>\incGamma@{n+1}{z} = n!e^{-z}e_{n}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{n+1}{z} = n!e^{-z}e_{n}(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(n + 1, z) = factorial(n)*exp(- z)*exp(1)[n]*(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[n + 1, z] == (n)!*Exp[- z]*Subscript[E, n]*(z)</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.7896317094254578, -0.19173078621885742], Times[Complex[-0.42050290937849244, -0.009925196319850484], Subscript[2.718281828459045, 1]]]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[1.9384670225780305, -0.16461464559793018], Times[Complex[-0.8410058187569849, -0.019850392639700967], Subscript[2.718281828459045, 2]]]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E9 8.4.E9] || [[Item:Q2503|<math>\normincGammaP@{n+1}{z} = 1-e^{-z}e_{n}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{n+1}{z} = 1-e^{-z}e_{n}(z)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(GAMMA(n + 1)-GAMMA(n + 1, z))/GAMMA(n + 1) = 1 - exp(- z)*exp(1)[n]*(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[n + 1, 0, z] == 1 - Exp[- z]*Subscript[E, n]*(z)</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.7896317094254579, 0.1917307862188573], Times[Complex[0.42050290937849244, 0.009925196319850484], Subscript[2.718281828459045, 1]]]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.9692335112890152, 0.08230732279896512], Times[Complex[0.42050290937849244, 0.009925196319850484], Subscript[2.718281828459045, 2]]]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E10 8.4.E10] || [[Item:Q2504|<math>\normincGammaQ@{n+1}{z} = e^{-z}e_{n}(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaQ@{n+1}{z} = e^{-z}e_{n}(z)</syntaxhighlight> || <math>\realpart@@{(n+1)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(n + 1, z)/GAMMA(n + 1) = exp(- z)*exp(1)[n]*(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[n + 1, z] == Exp[- z]*Subscript[E, n]*(z)</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.7896317094254579, -0.1917307862188573], Times[Complex[-0.42050290937849244, -0.009925196319850484], Subscript[2.718281828459045, 1]]]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.9692335112890152, -0.08230732279896512], Times[Complex[-0.42050290937849244, -0.009925196319850484], Subscript[2.718281828459045, 2]]]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E12 8.4.E12] || [[Item:Q2506|<math>\scincgamma@{-n}{z} = z^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scincgamma@{-n}{z} = z^{n}</syntaxhighlight> || <math>\realpart@@{(-n)} > 0</math> || <syntaxhighlight lang=mathematica>(z)^(-(- n))*(GAMMA(- n)-GAMMA(- n, z))/GAMMA(- n) = (z)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || -
-|-
-| [https://dlmf.nist.gov/8.4.E13 8.4.E13] || [[Item:Q2507|<math>\incGamma@{1-n}{z} = z^{1-n}\genexpintE{n}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{1-n}{z} = z^{1-n}\genexpintE{n}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(1 - n, z) = (z)^(1 - n)* Ei(n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[1 - n, z] == (z)^(1 - n)* ExpIntegralE[n, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.4.E14 8.4.E14] || [[Item:Q2508|<math>\normincGammaQ@{n+\tfrac{1}{2}}{z^{2}} = \erfc@{z}+\frac{e^{-z^{2}}}{\sqrt{\pi}}\sum_{k=1}^{n}\frac{z^{2k-1}}{\Pochhammersym{\tfrac{1}{2}}{k}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaQ@{n+\tfrac{1}{2}}{z^{2}} = \erfc@{z}+\frac{e^{-z^{2}}}{\sqrt{\pi}}\sum_{k=1}^{n}\frac{z^{2k-1}}{\Pochhammersym{\tfrac{1}{2}}{k}}</syntaxhighlight> || <math>\realpart@@{(n+\tfrac{1}{2})} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(n +(1)/(2), (z)^(2))/GAMMA(n +(1)/(2)) = erfc(z)+(exp(- (z)^(2)))/(sqrt(Pi))*sum(((z)^(2*k - 1))/(pochhammer((1)/(2), k)), k = 1..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[n +Divide[1,2], (z)^(2)] == Erfc[z]+Divide[Exp[- (z)^(2)],Sqrt[Pi]]*Sum[Divide[(z)^(2*k - 1),Pochhammer[Divide[1,2], k]], {k, 1, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.704415567+1.043704337*I
-Test Values: {z = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .97393781e-1-.8458491548*I
-Test Values: {z = -1/2+1/2*I*3^(1/2), n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.7044155650581054, 1.0437043365740406]
-Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.09739377924871273, -0.8458491528064774]
-Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.4.E15 8.4.E15] || [[Item:Q2509|<math>\incGamma@{-n}{z} = \frac{(-1)^{n}}{n!}\left(\expintE@{z}-e^{-z}\sum_{k=0}^{n-1}\frac{(-1)^{k}k!}{z^{k+1}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{-n}{z} = \frac{(-1)^{n}}{n!}\left(\expintE@{z}-e^{-z}\sum_{k=0}^{n-1}\frac{(-1)^{k}k!}{z^{k+1}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(- n, z) = ((- 1)^(n))/(factorial(n))*(Ei(z)- exp(- z)*sum(((- 1)^(k)* factorial(k))/((z)^(k + 1)), k = 0..n - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[- n, z] == Divide[(- 1)^(n),(n)!]*(ExpIntegralE[1, z]- Exp[- z]*Sum[Divide[(- 1)^(k)* (k)!,(z)^(k + 1)], {k, 0, n - 1}, GenerateConditions->None])</syntaxhighlight> || Failure || Failure || Manual Skip! || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.5.E1 8.5.E1] || [[Item:Q2510|<math>\incgamma@{a}{z} = a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == (a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.5.E1 8.5.E1] || [[Item:Q2510|<math>a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z} = a^{-1}z^{a}\KummerconfhyperM@{a}{1+a}{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a^{-1}z^{a}e^{-z}\KummerconfhyperM@{1}{1+a}{z} = a^{-1}z^{a}\KummerconfhyperM@{a}{1+a}{-z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(a)^(- 1)* (z)^(a)* exp(- z)*KummerM(1, 1 + a, z) = (a)^(- 1)* (z)^(a)* KummerM(a, 1 + a, - z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(a)^(- 1)* (z)^(a)* Exp[- z]*Hypergeometric1F1[1, 1 + a, z] == (a)^(- 1)* (z)^(a)* Hypergeometric1F1[a, 1 + a, - z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.5.E2 8.5.E2] || [[Item:Q2511|<math>\scincgamma@{a}{z} = e^{-z}\OlverconfhyperM@{1}{1+a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scincgamma@{a}{z} = e^{-z}\OlverconfhyperM@{1}{1+a}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = exp(- z)*KummerM(1, 1 + a, z)/GAMMA(1 + a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
-|-
-| [https://dlmf.nist.gov/8.5.E2 8.5.E2] || [[Item:Q2511|<math>e^{-z}\OlverconfhyperM@{1}{1+a}{z} = \OlverconfhyperM@{a}{1+a}{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-z}\OlverconfhyperM@{1}{1+a}{z} = \OlverconfhyperM@{a}{1+a}{-z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>exp(- z)*KummerM(1, 1 + a, z)/GAMMA(1 + a) = KummerM(a, 1 + a, - z)/GAMMA(1 + a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- z]*Hypergeometric1F1Regularized[1, 1 + a, z] == Hypergeometric1F1Regularized[a, 1 + a, - z]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 42]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.5.E3 8.5.E3] || [[Item:Q2512|<math>\incGamma@{a}{z} = e^{-z}\KummerconfhyperU@{1-a}{1-a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = e^{-z}\KummerconfhyperU@{1-a}{1-a}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = exp(- z)*KummerU(1 - a, 1 - a, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Exp[- z]*HypergeometricU[1 - a, 1 - a, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 42]
-|-
-| [https://dlmf.nist.gov/8.5.E3 8.5.E3] || [[Item:Q2512|<math>e^{-z}\KummerconfhyperU@{1-a}{1-a}{z} = z^{a}e^{-z}\KummerconfhyperU@{1}{1+a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-z}\KummerconfhyperU@{1-a}{1-a}{z} = z^{a}e^{-z}\KummerconfhyperU@{1}{1+a}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(- z)*KummerU(1 - a, 1 - a, z) = (z)^(a)* exp(- z)*KummerU(1, 1 + a, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- z]*HypergeometricU[1 - a, 1 - a, z] == (z)^(a)* Exp[- z]*HypergeometricU[1, 1 + a, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 42]
-|-
-| [https://dlmf.nist.gov/8.5.E4 8.5.E4] || [[Item:Q2513|<math>\incgamma@{a}{z} = a^{-1}z^{\frac{1}{2}a-\frac{1}{2}}e^{-\frac{1}{2}z}\WhittakerconfhyperM{\frac{1}{2}a-\frac{1}{2}}{\frac{1}{2}a}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = a^{-1}z^{\frac{1}{2}a-\frac{1}{2}}e^{-\frac{1}{2}z}\WhittakerconfhyperM{\frac{1}{2}a-\frac{1}{2}}{\frac{1}{2}a}@{z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (a)^(- 1)* (z)^((1)/(2)*a -(1)/(2))* exp(-(1)/(2)*z)*WhittakerM((1)/(2)*a -(1)/(2), (1)/(2)*a, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == (a)^(- 1)* (z)^(Divide[1,2]*a -Divide[1,2])* Exp[-Divide[1,2]*z]*WhittakerM[Divide[1,2]*a -Divide[1,2], Divide[1,2]*a, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.5.E5 8.5.E5] || [[Item:Q2514|<math>\incGamma@{a}{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}a-\frac{1}{2}}\WhittakerconfhyperW{\frac{1}{2}a-\frac{1}{2}}{\frac{1}{2}a}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = e^{-\frac{1}{2}z}z^{\frac{1}{2}a-\frac{1}{2}}\WhittakerconfhyperW{\frac{1}{2}a-\frac{1}{2}}{\frac{1}{2}a}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = exp(-(1)/(2)*z)*(z)^((1)/(2)*a -(1)/(2))* WhittakerW((1)/(2)*a -(1)/(2), (1)/(2)*a, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Exp[-Divide[1,2]*z]*(z)^(Divide[1,2]*a -Divide[1,2])* WhittakerW[Divide[1,2]*a -Divide[1,2], Divide[1,2]*a, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 42]
-|-
-| [https://dlmf.nist.gov/8.6.E1 8.6.E1] || [[Item:Q2515|<math>\incgamma@{a}{z} = \frac{z^{a}}{\sin@{\pi a}}\int_{0}^{\pi}e^{z\cos@@{t}}\cos@{at+z\sin@@{t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = \frac{z^{a}}{\sin@{\pi a}}\int_{0}^{\pi}e^{z\cos@@{t}}\cos@{at+z\sin@@{t}}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = ((z)^(a))/(sin(Pi*a))*int(exp(z*cos(t))*cos(a*t + z*sin(t)), t = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == Divide[(z)^(a),Sin[Pi*a]]*Integrate[Exp[z*Cos[t]]*Cos[a*t + z*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.922649672+.1964472815*I
-Test Values: {a = .5, z = 1/2*3^(1/2)+1/2*I, a = 3/2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.511118576+1.941926371*I
-Test Values: {a = .5, z = -1/2+1/2*I*3^(1/2), a = 3/2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.6.E2 8.6.E2] || [[Item:Q2516|<math>\incgamma@{a}{z} = z^{\frac{1}{2}a}\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}a-1}\BesselJ{a}@{2\sqrt{zt}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = z^{\frac{1}{2}a}\int_{0}^{\infty}e^{-t}t^{\frac{1}{2}a-1}\BesselJ{a}@{2\sqrt{zt}}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (z)^((1)/(2)*a)* int(exp(- t)*(t)^((1)/(2)*a - 1)* BesselJ(a, 2*sqrt(z*t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == (z)^(Divide[1,2]*a)* Integrate[Exp[- t]*(t)^(Divide[1,2]*a - 1)* BesselJ[a, 2*Sqrt[z*t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 21] || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.6.E3 8.6.E3] || [[Item:Q2517|<math>\incgamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{-at-ze^{-t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{-at-ze^{-t}}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (z)^(a)* int(exp(- a*t - z*exp(- t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == (z)^(a)* Integrate[Exp[- a*t - z*Exp[- t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 21] || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.6.E4 8.6.E4] || [[Item:Q2518|<math>\incGamma@{a}{z} = \frac{z^{a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = \frac{z^{a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}\frac{t^{-a}e^{-t}}{z+t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \pi, \realpart@@{a} < 1, \realpart@@{(1-a)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = ((z)^(a)* exp(- z))/(GAMMA(1 - a))*int(((t)^(- a)* exp(- t))/(z + t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Divide[(z)^(a)* Exp[- z],Gamma[1 - a]]*Integrate[Divide[(t)^(- a)* Exp[- t],z + t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 28]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = -1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = -1.5, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 28]
-|-
-| [https://dlmf.nist.gov/8.6.E5 8.6.E5] || [[Item:Q2519|<math>\incGamma@{a}{z} = z^{a}e^{-z}\int_{0}^{\infty}\frac{e^{-zt}}{(1+t)^{1-a}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = z^{a}e^{-z}\int_{0}^{\infty}\frac{e^{-zt}}{(1+t)^{1-a}}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = (z)^(a)* exp(- z)*int((exp(- z*t))/((1 + t)^(1 - a)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == (z)^(a)* Exp[- z]*Integrate[Divide[Exp[- z*t],(1 + t)^(1 - a)], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 30]
-|-
-| [https://dlmf.nist.gov/8.6.E6 8.6.E6] || [[Item:Q2520|<math>\incGamma@{a}{z} = \frac{2z^{\frac{1}{2}a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}e^{-t}t^{-\frac{1}{2}a}\modBesselK{a}@{2\sqrt{zt}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = \frac{2z^{\frac{1}{2}a}e^{-z}}{\EulerGamma@{1-a}}\int_{0}^{\infty}e^{-t}t^{-\frac{1}{2}a}\modBesselK{a}@{2\sqrt{zt}}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} < 1, \realpart@@{(1-a)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = (2*(z)^((1)/(2)*a)* exp(- z))/(GAMMA(1 - a))*int(exp(- t)*(t)^(-(1)/(2)*a)* BesselK(a, 2*sqrt(z*t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Divide[2*(z)^(Divide[1,2]*a)* Exp[- z],Gamma[1 - a]]*Integrate[Exp[- t]*(t)^(-Divide[1,2]*a)* BesselK[a, 2*Sqrt[z*t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 28]
-|-
-| [https://dlmf.nist.gov/8.6.E7 8.6.E7] || [[Item:Q2521|<math>\incGamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{at-ze^{t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = z^{a}\int_{0}^{\infty}\exp@{at-ze^{t}}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = (z)^(a)* int(exp(a*t - z*exp(t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == (z)^(a)* Integrate[Exp[a*t - z*Exp[t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 30] || Successful [Tested: 30]
-|-
-| [https://dlmf.nist.gov/8.6.E8 8.6.E8] || [[Item:Q2522|<math>\incgamma@{a}{z} = \frac{-\iunit z^{a}}{2\sin@{\pi a}}\int_{-1}^{(0+)}t^{a-1}e^{zt}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = \frac{-\iunit z^{a}}{2\sin@{\pi a}}\int_{-1}^{(0+)}t^{a-1}e^{zt}\diff{t}</syntaxhighlight> || <math>z \neq 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (- I*(z)^(a))/(2*sin(Pi*a))*int((t)^(a - 1)* exp(z*t), t = - 1..(0 +))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == Divide[- I*(z)^(a),2*Sin[Pi*a]]*Integrate[(t)^(a - 1)* Exp[z*t], {t, - 1, (0 +)}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/8.6.E9 8.6.E9] || [[Item:Q2523|<math>\incGamma@{-a}{ze^{+\pi i}} = \frac{e^{z}e^{-\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{-a}{ze^{+\pi i}} = \frac{e^{z}e^{-\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0, \realpart@@{a} > -1, \realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(- a, z*exp(+ Pi*I)) = (exp(z)*exp(- Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[- a, z*Exp[+ Pi*I]] == Divide[Exp[z]*Exp[- Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 20]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = 1.5, z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.6.E9 8.6.E9] || [[Item:Q2523|<math>\incGamma@{-a}{ze^{-\pi i}} = \frac{e^{z}e^{+\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{-a}{ze^{-\pi i}} = \frac{e^{z}e^{+\pi\iunit a}}{\EulerGamma@{1+a}}\int_{0}^{\infty}\frac{t^{a}e^{-zt}}{t-1}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0, \realpart@@{a} > -1, \realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(- a, z*exp(- Pi*I)) = (exp(z)*exp(+ Pi*I*a))/(GAMMA(1 + a))*int(((t)^(a)* exp(- z*t))/(t - 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[- a, z*Exp[- Pi*I]] == Divide[Exp[z]*Exp[+ Pi*I*a],Gamma[1 + a]]*Integrate[Divide[(t)^(a)* Exp[- z*t],t - 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 20]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = 1.5, z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.6.E10 8.6.E10] || [[Item:Q2524|<math>\incgamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{s}}{a-s}z^{a-s}\diff{s}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\frac{\EulerGamma@{s}}{a-s}z^{a-s}\diff{s}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{s} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (1)/(2*Pi*I)*int((GAMMA(s))/(a - s)*(z)^(a - s), s = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == Divide[1,2*Pi*I]*Integrate[Divide[Gamma[s],a - s]*(z)^(a - s), {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3508882474+.1990162824*I
-Test Values: {a = 1.5, c = -1.5, z = 1/2*3^(1/2)+1/2*I, a = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2281607298-.4280186861*I
-Test Values: {a = 1.5, c = -1.5, z = 1/2-1/2*I*3^(1/2), a = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.6.E11 8.6.E11] || [[Item:Q2525|<math>\incGamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+a}\frac{z^{-s}}{s}\diff{s}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = \frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+a}\frac{z^{-s}}{s}\diff{s}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{(s+a)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = (1)/(2*Pi*I)*int(GAMMA(s + a)*((z)^(- s))/(s), s = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Divide[1,2*Pi*I]*Integrate[Gamma[s + a]*Divide[(z)^(- s),s], {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1072320848e-1-.1480251451*I
-Test Values: {a = -1.5, c = -1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2224046553+.6479031822e-1*I
-Test Values: {a = -1.5, c = -1.5, z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.6.E12 8.6.E12] || [[Item:Q2526|<math>\incGamma@{a}{z} = -\frac{z^{a-1}e^{-z}}{\EulerGamma@{1-a}}\*\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+1-a}\frac{\pi z^{-s}}{\sin@{\pi s}}\diff{s}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = -\frac{z^{a-1}e^{-z}}{\EulerGamma@{1-a}}\*\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\EulerGamma@{s+1-a}\frac{\pi z^{-s}}{\sin@{\pi s}}\diff{s}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{3}{2}\pi, \realpart@@{(s+1-a)} > 0, \realpart@@{(1-a)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = -((z)^(a - 1)* exp(- z))/(GAMMA(1 - a))*(1)/(2*Pi*I)*int(GAMMA(s + 1 - a)*(Pi*(z)^(- s))/(sin(Pi*s)), s = c - I*infinity..c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == -Divide[(z)^(a - 1)* Exp[- z],Gamma[1 - a]]*Divide[1,2*Pi*I]*Integrate[Gamma[s + 1 - a]*Divide[Pi*(z)^(- s),Sin[Pi*s]], {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [168 / 168]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1072320848e-1-.1480251451*I
-Test Values: {a = -1.5, c = -1.5, z = 1/2*3^(1/2)+1/2*I, a = -1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7867555591e-1+.8824866094*I
-Test Values: {a = -1.5, c = -1.5, z = -1/2+1/2*I*3^(1/2), a = -1}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.7.E1 8.7.E1] || [[Item:Q2527|<math>\scincgamma@{a}{z} = e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\scincgamma@{a}{z} = e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}</syntaxhighlight> || <math>\realpart@@{(a+k+1)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
-|-
-| [https://dlmf.nist.gov/8.7.E1 8.7.E1] || [[Item:Q2527|<math>e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}} = \frac{1}{\EulerGamma@{a}}\sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(a+k)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}} = \frac{1}{\EulerGamma@{a}}\sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(a+k)}</syntaxhighlight> || <math>\realpart@@{(a+k+1)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity) = (1)/(GAMMA(a))*sum(((- z)^(k))/(factorial(k)*(a + k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}, GenerateConditions->None] == Divide[1,Gamma[a]]*Sum[Divide[(- z)^(k),(k)!*(a + k)], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.7.E2 8.7.E2] || [[Item:Q2528|<math>\incgamma@{a}{x+y}-\incgamma@{a}{x} = \incGamma@{a}{x}-\incGamma@{a}{x+y}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{x+y}-\incgamma@{a}{x} = \incGamma@{a}{x}-\incGamma@{a}{x+y}</syntaxhighlight> || <math>|y| < |x|, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, x + y)- GAMMA(a)-GAMMA(a, x) = GAMMA(a, x)- GAMMA(a, x + y)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, x + y]- Gamma[a, 0, x] == Gamma[a, x]- Gamma[a, x + y]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6941375518
-Test Values: {a = 1.5, x = 1.5, y = -.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.6941375518
-Test Values: {a = 1.5, x = 1.5, y = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 18]
-|-
-| [https://dlmf.nist.gov/8.7.E2 8.7.E2] || [[Item:Q2528|<math>\incGamma@{a}{x}-\incGamma@{a}{x+y} = e^{-x}x^{a-1}\sum_{n=0}^{\infty}\frac{\Pochhammersym{1-a}{n}}{(-x)^{n}}(1-e^{-y}e_{n}(y))</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{x}-\incGamma@{a}{x+y} = e^{-x}x^{a-1}\sum_{n=0}^{\infty}\frac{\Pochhammersym{1-a}{n}}{(-x)^{n}}(1-e^{-y}e_{n}(y))</syntaxhighlight> || <math>|y| < |x|, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, x)- GAMMA(a, x + y) = exp(- x)*(x)^(a - 1)* sum((pochhammer(1 - a, n))/((- x)^(n))*(1 - exp(- y)*exp(1)[n]*(y)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, x]- Gamma[a, x + y] == Exp[- x]*(x)^(a - 1)* Sum[Divide[Pochhammer[1 - a, n],(- x)^(n)]*(1 - Exp[- y]*Subscript[E, n]*(y)), {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || Skip - symbolical successful subtest || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.7.E3 8.7.E3] || [[Item:Q2529|<math>\incGamma@{a}{z} = \EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = \EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.7.E3 8.7.E3] || [[Item:Q2529|<math>\EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)} = \EulerGamma@{a}\left(1-z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerGamma@{a}-\sum_{k=0}^{\infty}\frac{(-1)^{k}z^{a+k}}{k!(a+k)} = \EulerGamma@{a}\left(1-z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{a+k+1}}\right)</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)- sum(((- 1)^(k)* (z)^(a + k))/(factorial(k)*(a + k)), k = 0..infinity) = GAMMA(a)*(1 - (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a]- Sum[Divide[(- 1)^(k)* (z)^(a + k),(k)!*(a + k)], {k, 0, Infinity}, GenerateConditions->None] == Gamma[a]*(1 - (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, Infinity}, GenerateConditions->None])</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.7.E6 8.7.E6] || [[Item:Q2532|<math>\incGamma@{a}{x} = x^{a}e^{-x}\sum_{n=0}^{\infty}\frac{\LaguerrepolyL[a]{n}@{x}}{n+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{x} = x^{a}e^{-x}\sum_{n=0}^{\infty}\frac{\LaguerrepolyL[a]{n}@{x}}{n+1}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, x) = (x)^(a)* exp(- x)*sum((LaguerreL(n, a, x))/(n + 1), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, x] == (x)^(a)* Exp[- x]*Sum[Divide[LaguerreL[n, a, x],n + 1], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.03483445061608508, Times[-0.1214566752420326, NSum[Times[Power[Plus[1, n], -1], LaguerreL[n, -1.5, 1.5]]
-Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[a, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[0.7498909754592095, Times[-1.7155277699214138, NSum[Times[Power[Plus[1, n], -1], LaguerreL[n, -1.5, 0.5]]
-Test Values: {n, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]]], {Rule[a, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.8.E1 8.8.E1] || [[Item:Q2533|<math>\incgamma@{a+1}{z} = a\incgamma@{a}{z}-z^{a}e^{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a+1}{z} = a\incgamma@{a}{z}-z^{a}e^{-z}</syntaxhighlight> || <math>\realpart@@{(a+1)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a + 1)-GAMMA(a + 1, z) = a*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a + 1, 0, z] == a*Gamma[a, 0, z]- (z)^(a)* Exp[- z]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2676693395+.995081412e-1*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.820738205+.231239721*I
-Test Values: {a = 1.5, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.8.E2 8.8.E2] || [[Item:Q2534|<math>\incGamma@{a+1}{z} = a\incGamma@{a}{z}+z^{a}e^{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a+1}{z} = a\incGamma@{a}{z}+z^{a}e^{-z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(a + 1, z) = a*GAMMA(a, z)+ (z)^(a)* exp(- z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a + 1, z] == a*Gamma[a, z]+ (z)^(a)* Exp[- z]</syntaxhighlight> || Failure || Successful || Successful [Tested: 42] || Successful [Tested: 42]
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.8.E3 8.8.E3] || [[Item:Q2535|<math>w(a+2,z)-(a+1+z)w(a+1,z)+azw(a,z) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(a+2,z)-(a+1+z)w(a+1,z)+azw(a,z) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(a + 2 , z)-(a + 1 + z)*w(a + 1 , z)+ azw(a , z) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[a + 2 , z]-(a + 1 + z)*w[a + 1 , z]+ azw[a , z] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.8.E4 8.8.E4] || [[Item:Q2536|<math>z\scincgamma@{a+1}{z} = \scincgamma@{a}{z}-\frac{e^{-z}}{\EulerGamma@{a+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\scincgamma@{a+1}{z} = \scincgamma@{a}{z}-\frac{e^{-z}}{\EulerGamma@{a+1}}</syntaxhighlight> || <math>\realpart@@{(a+1)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>z*(z)^(-(a + 1))*(GAMMA(a + 1)-GAMMA(a + 1, z))/GAMMA(a + 1) = (z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a)-(exp(- z))/(GAMMA(a + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Successful [Tested: 21] || -
-|-
-| [https://dlmf.nist.gov/8.8.E5 8.8.E5] || [[Item:Q2537|<math>\normincGammaP@{a+1}{z} = \normincGammaP@{a}{z}-\frac{z^{a}e^{-z}}{\EulerGamma@{a+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a+1}{z} = \normincGammaP@{a}{z}-\frac{z^{a}e^{-z}}{\EulerGamma@{a+1}}</syntaxhighlight> || <math>\realpart@@{(a+1)} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(a + 1)-GAMMA(a + 1, z))/GAMMA(a + 1) = (GAMMA(a)-GAMMA(a, z))/GAMMA(a)-((z)^(a)* exp(- z))/(GAMMA(a + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a + 1, 0, z] == GammaRegularized[a, 0, z]-Divide[(z)^(a)* Exp[- z],Gamma[a + 1]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 28] || Successful [Tested: 28]
-|-
-| [https://dlmf.nist.gov/8.8.E6 8.8.E6] || [[Item:Q2538|<math>\normincGammaQ@{a+1}{z} = \normincGammaQ@{a}{z}+\frac{z^{a}e^{-z}}{\EulerGamma@{a+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaQ@{a+1}{z} = \normincGammaQ@{a}{z}+\frac{z^{a}e^{-z}}{\EulerGamma@{a+1}}</syntaxhighlight> || <math>\realpart@@{(a+1)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a + 1, z)/GAMMA(a + 1) = GAMMA(a, z)/GAMMA(a)+((z)^(a)* exp(- z))/(GAMMA(a + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a + 1, z] == GammaRegularized[a, z]+Divide[(z)^(a)* Exp[- z],Gamma[a + 1]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 28] || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.8.E7 8.8.E7] || [[Item:Q2539|<math>\incgamma@{a+n}{z} = \Pochhammersym{a}{n}\incgamma@{a}{z}-z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a+n}}{\EulerGamma@{a+k+1}}z^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a+n}{z} = \Pochhammersym{a}{n}\incgamma@{a}{z}-z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a+n}}{\EulerGamma@{a+k+1}}z^{k}</syntaxhighlight> || <math>\realpart@@{(a+n)} > 0, \realpart@@{(a+k+1)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a + n)-GAMMA(a + n, z) = pochhammer(a, n)*GAMMA(a)-GAMMA(a, z)- (z)^(a)* exp(- z)*sum((GAMMA(a + n))/(GAMMA(a + k + 1))*(z)^(k), k = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a + n, 0, z] == Pochhammer[a, n]*Gamma[a, 0, z]- (z)^(a)* Exp[- z]*Sum[Divide[Gamma[a + n],Gamma[a + k + 1]]*(z)^(k), {k, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [63 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.2676693391+.995081412e-1*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.472181365+.5472947763*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 63]
-|-
-| [https://dlmf.nist.gov/8.8.E8 8.8.E8] || [[Item:Q2540|<math>\incgamma@{a}{z} = \frac{\EulerGamma@{a}}{\EulerGamma@{a-n}}\incgamma@{a-n}{z}-z^{a-1}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a}}{\EulerGamma@{a-k}}z^{-k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = \frac{\EulerGamma@{a}}{\EulerGamma@{a-n}}\incgamma@{a-n}{z}-z^{a-1}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a}}{\EulerGamma@{a-k}}z^{-k}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a-n)} > 0, \realpart@@{(a-k)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (GAMMA(a))/(GAMMA(a - n))*GAMMA(a - n)-GAMMA(a - n, z)- (z)^(a - 1)* exp(- z)*sum((GAMMA(a))/(GAMMA(a - k))*(z)^(- k), k = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == Divide[Gamma[a],Gamma[a - n]]*Gamma[a - n, 0, z]- (z)^(a - 1)* Exp[- z]*Sum[Divide[Gamma[a],Gamma[a - k]]*(z)^(- k), {k, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 14]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1265952281-.9976912441e-1*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .19739482e-1-.7595504274*I
-Test Values: {a = 1.5, z = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 14]
-|-
-| [https://dlmf.nist.gov/8.8.E9 8.8.E9] || [[Item:Q2541|<math>\incGamma@{a+n}{z} = \Pochhammersym{a}{n}\incGamma@{a}{z}+z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a+n}}{\EulerGamma@{a+k+1}}z^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a+n}{z} = \Pochhammersym{a}{n}\incGamma@{a}{z}+z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a+n}}{\EulerGamma@{a+k+1}}z^{k}</syntaxhighlight> || <math>\realpart@@{(a+n)} > 0, \realpart@@{(a+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a + n, z) = pochhammer(a, n)*GAMMA(a, z)+ (z)^(a)* exp(- z)*sum((GAMMA(a + n))/(GAMMA(a + k + 1))*(z)^(k), k = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a + n, z] == Pochhammer[a, n]*Gamma[a, z]+ (z)^(a)* Exp[- z]*Sum[Divide[Gamma[a + n],Gamma[a + k + 1]]*(z)^(k), {k, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 105]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.8.E10 8.8.E10] || [[Item:Q2542|<math>\incGamma@{a}{z} = \frac{\EulerGamma@{a}}{\EulerGamma@{a-n}}\incGamma@{a-n}{z}+z^{a-1}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a}}{\EulerGamma@{a-k}}z^{-k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = \frac{\EulerGamma@{a}}{\EulerGamma@{a-n}}\incGamma@{a-n}{z}+z^{a-1}e^{-z}\sum_{k=0}^{n-1}\frac{\EulerGamma@{a}}{\EulerGamma@{a-k}}z^{-k}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a-n)} > 0, \realpart@@{(a-k)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = (GAMMA(a))/(GAMMA(a - n))*GAMMA(a - n, z)+ (z)^(a - 1)* exp(- z)*sum((GAMMA(a))/(GAMMA(a - k))*(z)^(- k), k = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == Divide[Gamma[a],Gamma[a - n]]*Gamma[a - n, z]+ (z)^(a - 1)* Exp[- z]*Sum[Divide[Gamma[a],Gamma[a - k]]*(z)^(- k), {k, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 14] || Successful [Tested: 14]
-|-
-| [https://dlmf.nist.gov/8.8.E11 8.8.E11] || [[Item:Q2543|<math>\normincGammaP@{a+n}{z} = \normincGammaP@{a}{z}-z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{z^{k}}{\EulerGamma@{a+k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a+n}{z} = \normincGammaP@{a}{z}-z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{z^{k}}{\EulerGamma@{a+k+1}}</syntaxhighlight> || <math>\realpart@@{(a+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(a + n)-GAMMA(a + n, z))/GAMMA(a + n) = (GAMMA(a)-GAMMA(a, z))/GAMMA(a)- (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a + n, 0, z] == GammaRegularized[a, 0, z]- (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 126]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.8.E12 8.8.E12] || [[Item:Q2544|<math>\normincGammaQ@{a+n}{z} = \normincGammaQ@{a}{z}+z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{z^{k}}{\EulerGamma@{a+k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaQ@{a+n}{z} = \normincGammaQ@{a}{z}+z^{a}e^{-z}\sum_{k=0}^{n-1}\frac{z^{k}}{\EulerGamma@{a+k+1}}</syntaxhighlight> || <math>\realpart@@{(a+k+1)} > 0, \realpart@@{(a+n)} > 0, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a + n, z)/GAMMA(a + n) = GAMMA(a, z)/GAMMA(a)+ (z)^(a)* exp(- z)*sum(((z)^(k))/(GAMMA(a + k + 1)), k = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a + n, z] == GammaRegularized[a, z]+ (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Gamma[a + k + 1]], {k, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 63]
-|-
-| [https://dlmf.nist.gov/8.8.E13 8.8.E13] || [[Item:Q2545|<math>\deriv{}{z}\incgamma@{a}{z} = -\deriv{}{z}\incGamma@{a}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\incgamma@{a}{z} = -\deriv{}{z}\incGamma@{a}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>diff(GAMMA(a)-GAMMA(a, z), z) = - diff(GAMMA(a, z), z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Gamma[a, 0, z], z] == - D[Gamma[a, z], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.8.E13 8.8.E13] || [[Item:Q2545|<math>-\deriv{}{z}\incGamma@{a}{z} = z^{a-1}e^{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\deriv{}{z}\incGamma@{a}{z} = z^{a-1}e^{-z}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>- diff(GAMMA(a, z), z) = (z)^(a - 1)* exp(- z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- D[Gamma[a, z], z] == (z)^(a - 1)* Exp[- z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.8.E15 8.8.E15] || [[Item:Q2547|<math>\deriv[n]{}{z}(z^{-a}\incgamma@{a}{z}) = (-1)^{n}z^{-a-n}\incgamma@{a+n}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n]{}{z}(z^{-a}\incgamma@{a}{z}) = (-1)^{n}z^{-a-n}\incgamma@{a+n}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a+n)} > 0</math> || <syntaxhighlight lang=mathematica>diff((z)^(- a)* GAMMA(a)-GAMMA(a, z), [z$(n)]) = (- 1)^(n)* (z)^(- a - n)* GAMMA(a + n)-GAMMA(a + n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(z)^(- a)* Gamma[a, 0, z], {z, n}] == (- 1)^(n)* (z)^(- a - n)* Gamma[a + n, 0, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [63 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.615357258-.2793504168*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 3.050292670-.1918135000*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [63 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.20573036539123668, -0.07193062032175179], Inactive[Sum][Times[Power[Complex[0.8660254037844387, 0.49999999999999994], Plus[-1.5, Times[-1.0, K[1.0]]]], Binomial[1.0, K[1.0]], D[Complex[0.3508882473022298, 0.19901628242832037]
-Test Values: {Complex[0.8660254037844387, 0.49999999999999994], Plus[1.0, Times[-1.0, K[1.0]]]}], FactorialPower[-1.5, K[1.0]]], {K[1.0], 0.0, 1.0}]], {Rule[a, 1.5], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.13665910465469025, 0.05369371428345661], Inactive[Sum][Times[Power[Complex[0.8660254037844387, 0.49999999999999994], Plus[-1.5, Times[-1.0, K[1.0]]]], Binomial[2.0, K[1.0]], D[Complex[0.3508882473022298, 0.19901628242832037]
-Test Values: {Complex[0.8660254037844387, 0.49999999999999994], Plus[2.0, Times[-1.0, K[1.0]]]}], FactorialPower[-1.5, K[1.0]]], {K[1.0], 0.0, 2.0}]], {Rule[a, 1.5], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.8.E16 8.8.E16] || [[Item:Q2548|<math>\deriv[n]{}{z}(z^{-a}\incGamma@{a}{z}) = (-1)^{n}z^{-a-n}\incGamma@{a+n}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n]{}{z}(z^{-a}\incGamma@{a}{z}) = (-1)^{n}z^{-a-n}\incGamma@{a+n}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff((z)^(- a)* GAMMA(a, z), [z$(n)]) = (- 1)^(n)* (z)^(- a - n)* GAMMA(a + n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[(z)^(- a)* Gamma[a, z], {z, n}] == (- 1)^(n)* (z)^(- a - n)* Gamma[a + n, z]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [111 / 126]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.14584260074790834, -0.14889469354125948], Times[Complex[0.9659258262890683, 0.25881904510252074], DifferenceRoot[Function[{, }
-Test Values: {Equal[Plus[Times[-1, , Plus[-1, Times[-1, ], 1], Plus[Times[-1, ], 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], []], Times[-1, Plus[-1, Times[-1, ], 1], Plus[1, Times[3, ], Times[3, Power[, 2]], Power[, 3], Times[-2, -1.5], Times[-4, , -1.5], Times[-2, Power[, 2], -1.5], Power[-1.5, 2], Times[, Power[-1.5, 2]], Times[-1, 1], Times[-2, , 1], Times[-1, Power[, 2], 1], Times[-1.5, 1], Times[, -1.5, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[2, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, , -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, 1, Power[E, Times[Complex[0, Rational[1, 6]], <syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.19291890162425956, 0.2582696599924231], Times[Complex[1.9318516525781366, -0.5176380902050415], DifferenceRoot[Function[{, }
-Test Values: {Equal[Plus[Times[-1, , Plus[-1, Times[-1, ], 2], Plus[Times[-1, ], 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], []], Times[-1, Plus[-1, Times[-1, ], 2], Plus[1, Times[3, ], Times[3, Power[, 2]], Power[, 3], Times[-2, -1.5], Times[-4, , -1.5], Times[-2, Power[, 2], -1.5], Power[-1.5, 2], Times[, Power[-1.5, 2]], Times[-1, 2], Times[-2, , 2], Times[-1, Power[, 2], 2], Times[-1.5, 2], Times[, -1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[2, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, Power[, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, , -1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-2, , 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[1, ]]], Times[Plus[1, ], Plus[-1, Times[-1, ], -1.5, 2], Plus[5, Times[6, ], Times[2, Power[, 2]], Times[-3, -1.5], Times[-2, , -1.5], Times[-3, 2], Times[-2, , 2], Times[-1.5, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Times[, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[2, ]]], Times[Plus[1, ], Plus[2, ], Plus[-2, Times[-1, ], -1.5, 2], Plus[-1, Times[-1, ], -1.5, 2], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Binomial[Times[-1, -1.5], 2], Gamma[-1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Times[Binomial[Times[-1, -1.5], 2], Plus[Times[Power[E, Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], 2, Power[Plus[-1, -1.5, 2], -1], Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], -1.5]], Gamma[-1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][3.0]]], {Rule[a, -1.5], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.8.E17 8.8.E17] || [[Item:Q2549|<math>\deriv[n]{}{z}(e^{z}\incgamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incgamma@{a-n}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n]{}{z}(e^{z}\incgamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incgamma@{a-n}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a-n)} > 0</math> || <syntaxhighlight lang=mathematica>diff(exp(z)*GAMMA(a)-GAMMA(a, z), [z$(n)]) = (- 1)^(n)* pochhammer(1 - a, n)*exp(z)*GAMMA(a - n)-GAMMA(a - n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Exp[z]*Gamma[a, 0, z], {z, n}] == (- 1)^(n)* Pochhammer[1 - a, n]*Exp[z]*Gamma[a - n, 0, z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 14]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6619339064-.2987854069*I
-Test Values: {a = 1.5, z = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.661215891-1.222029870*I
-Test Values: {a = 1.5, z = -1/2+1/2*I*3^(1/2), n = 1}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 14]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-1.471179750131411, -1.0739918488339026], Inactive[Sum][Times[Complex[2.0864022336812553, 1.1398067350757155], Binomial[1.0, K[1.0]], D[Complex[0.3508882473022298, 0.19901628242832037]
-Test Values: {Complex[0.8660254037844387, 0.49999999999999994], Plus[1.0, Times[-1.0, K[1.0]]]}]], {K[1.0], 0.0, 1.0}]], {Rule[a, 1.5], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.01045242262446705, -0.698806597134537], Inactive[Sum][Times[Complex[0.3929465558343552, 0.4620307840711054], Binomial[1.0, K[1.0]], D[Complex[-0.7552494829576352, 0.46247944264186114]
-Test Values: {Complex[-0.4999999999999998, 0.8660254037844387], Plus[1.0, Times[-1.0, K[1.0]]]}]], {K[1.0], 0.0, 1.0}]], {Rule[a, 1.5], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.8.E18 8.8.E18] || [[Item:Q2550|<math>\deriv[n]{}{z}(z^{a}e^{z}\scincgamma@{a}{z}) = z^{a-n}e^{z}\scincgamma@{a-n}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n]{}{z}(z^{a}e^{z}\scincgamma@{a}{z}) = z^{a-n}e^{z}\scincgamma@{a-n}{z}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a-n)} > 0</math> || <syntaxhighlight lang=mathematica>diff((z)^(a)* exp(z)*(z)^(-(a))*(GAMMA(a)-GAMMA(a, z))/GAMMA(a), [z$(n)]) = (z)^(a - n)* exp(z)*(z)^(-(a - n))*(GAMMA(a - n)-GAMMA(a - n, z))/GAMMA(a - n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Successful [Tested: 14] || -
-|-
-| [https://dlmf.nist.gov/8.8.E19 8.8.E19] || [[Item:Q2551|<math>\deriv[n]{}{z}(e^{z}\incGamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incGamma@{a-n}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[n]{}{z}(e^{z}\incGamma@{a}{z}) = (-1)^{n}\Pochhammersym{1-a}{n}e^{z}\incGamma@{a-n}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(exp(z)*GAMMA(a, z), [z$(n)]) = (- 1)^(n)* pochhammer(1 - a, n)*exp(z)*GAMMA(a - n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Exp[z]*Gamma[a, z], {z, n}] == (- 1)^(n)* Pochhammer[1 - a, n]*Exp[z]*Gamma[a - n, z]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 126]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.06772606154573046, -0.6693082179083164], Times[Complex[2.0864022336812553, 1.1398067350757155], DifferenceRoot[Function[{, }
-Test Values: {Equal[Plus[Times[-1, , Plus[-1, Times[-1, ], 1], Plus[Times[-1, ], 1], []], Times[Plus[-1, Times[-1, ], 1], Plus[-1, Times[-2, ], Times[-2, Power[, 2]], -1.5, Times[, -1.5], Times[, 1], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[1, ]]], Times[-1, Plus[1, ], Plus[1, Times[2, ], Power[, 2], Times[-1, -1.5], Times[-1, , -1.5], Times[-1, 1], Times[-1, , 1], Times[-1.5, 1], Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, 1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[2, ]]], Times[Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1<syntaxhighlight lang=mathematica>Result: Plus[Complex[0.714773674302028, 1.7455063478143567], Times[Complex[4.172804467362511, 2.279613470151431], DifferenceRoot[Function[{, }
-Test Values: {Equal[Plus[Times[-1, , Plus[-1, Times[-1, ], 2], Plus[Times[-1, ], 2], []], Times[Plus[-1, Times[-1, ], 2], Plus[-1, Times[-2, ], Times[-2, Power[, 2]], -1.5, Times[, -1.5], Times[, 2], Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[1, ]]], Times[-1, Plus[1, ], Plus[1, Times[2, ], Power[, 2], Times[-1, -1.5], Times[-1, , -1.5], Times[-1, 2], Times[-1, , 2], Times[-1.5, 2], Times[3, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[2, , Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Times[-1, 2, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], [Plus[2, ]]], Times[Plus[1, ], Plus[2, ], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], [Plus[3, ]]]], 0], Equal[[0], 0], Equal[[1], Times[Power[Factorial[2], -1], Gamma[-1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]], Equal[[2], Times[Power[Factorial[2], -1], Plus[Times[-1, Power[E, Times[-1, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], 2, Power[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Plus[-1, -1.5]]], Gamma[-1.5, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]]]}]][3.0]]], {Rule[a, -1.5], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10.E1 8.10.E1] || [[Item:Q2554|<math>x^{1-a}e^{x}\incGamma@{a}{x} \leq 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} \leq 1</syntaxhighlight> || <math>x > 0, 0 < a, a \leq 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) <= 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] <= 1</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/8.10.E2 8.10.E2] || [[Item:Q2555|<math>\incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{x} \geq \frac{x^{a-1}}{a}(1-e^{-x})</syntaxhighlight> || <math>x > 0, 0 < a, a \leq 1, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, x) >= ((x)^(a - 1))/(a)*(1 - exp(- x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, x] >= Divide[(x)^(a - 1),a]*(1 - Exp[- x])</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/8.10.E3 8.10.E3] || [[Item:Q2556|<math>x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} = 1+\frac{a-1}{x}\vartheta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) = 1 +(a - 1)/(x)*vartheta</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] == 1 +Divide[a - 1,x]*\[CurlyTheta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8735840245+.8333333335*I
-Test Values: {a = -1.5, x = 1.5, vartheta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.403124983+1.443375674*I
-Test Values: {a = -1.5, x = 1.5, vartheta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8735840235649492, 0.8333333333333331]
-Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.4031249827424481, 1.4433756729740643]
-Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϑ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10.E4 8.10.E4] || [[Item:Q2557|<math>0 < \vartheta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>0 < \vartheta</syntaxhighlight> || <math>x > 0, a \leq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < vartheta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">0 < \[CurlyTheta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{n} < x^{1-a}e^{x}\incGamma@{a}{x}</syntaxhighlight> || <math>x > 0, a < 1</math> || <syntaxhighlight lang=mathematica>A[n](<)*(x)^(1 - a)* exp(x)*GAMMA(a, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, n][<]*(x)^(1 - a)* Exp[x]*Gamma[a, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [75 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.5 < .4302083505
-Test Values: {a = -1.5, x = 1.5, A[n] = 1.5, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.5 < .4302083505
-Test Values: {a = -1.5, x = 1.5, A[n] = 1.5, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [195 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Less[Complex[0.8660254037844387, 0.49999999999999994], 0.43020835059088497]
-Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Less[Complex[0.8660254037844387, 0.49999999999999994], 0.43020835059088497]
-Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[A, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10.E5 8.10.E5] || [[Item:Q2558|<math>x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} < B_{n}</syntaxhighlight> || <math>x > 0, a < 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) < B[n]</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] < Subscript[B, n]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [105 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4302083505 < -1.5
-Test Values: {a = -1.5, x = 1.5, B[n] = -1.5, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4302083505 < -1.5
-Test Values: {a = -1.5, x = 1.5, B[n] = -1.5, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [225 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Less[0.43020835059088497, Complex[0.8660254037844387, 0.49999999999999994]]
-Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Less[0.43020835059088497, Complex[0.8660254037844387, 0.49999999999999994]]
-Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[B, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex1 8.10#Ex1] || [[Item:Q2559|<math>A_{1} = \frac{x}{x+1-a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1} = \frac{x}{x+1-a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[1] = (x)/(x + 1 - a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 1] == Divide[x,x + 1 - a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex2 8.10#Ex2] || [[Item:Q2560|<math>B_{1} = \frac{x+1}{x+2-a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1} = \frac{x+1}{x+2-a}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[1] = (x + 1)/(x + 2 - a)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 1] == Divide[x + 1,x + 2 - a]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex3 8.10#Ex3] || [[Item:Q2561|<math>A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2} = \frac{x(x+3-a)}{x^{2}+2(2-a)x+(1-a)(2-a)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[2] = (x*(x + 3 - a))/((x)^(2)+ 2*(2 - a)*x +(1 - a)*(2 - a))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 2] == Divide[x*(x + 3 - a),(x)^(2)+ 2*(2 - a)*x +(1 - a)*(2 - a)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10#Ex4 8.10#Ex4] || [[Item:Q2562|<math>B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2} = \frac{x^{2}+(5-a)x+2}{x^{2}+2(3-a)x+(2-a)(3-a)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">B[2] = ((x)^(2)+(5 - a)*x + 2)/((x)^(2)+ 2*(3 - a)*x +(2 - a)*(3 - a))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[B, 2] == Divide[(x)^(2)+(5 - a)*x + 2,(x)^(2)+ 2*(3 - a)*x +(2 - a)*(3 - a)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>I = \int_{0}^{x}t^{a-1}e^{t}\diff{t}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>I = int((t)^(a - 1)* exp(t), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>I == Integrate[(t)^(a - 1)* Exp[t], {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -2.374226751+.5000000000*I
-Test Values: {I = 1/2*3^(1/2)+1/2*I, a = 1.5, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5451660792+.5000000000*I
-Test Values: {I = 1/2*3^(1/2)+1/2*I, a = 1.5, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-2.240252154794788, -4.0113152157384396*^-17]
-Test Values: {Rule[Complex[0, 1], 1], Rule[a, 1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.240252154794788, -4.0113152157384396*^-17]
-Test Values: {Rule[Complex[0, 1], 2], Rule[a, 1.5], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10.E7 8.10.E7] || [[Item:Q2563|<math>\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{x}t^{a-1}e^{t}\diff{t} = \EulerGamma@{a}x^{a}\scincgamma@{a}{-x}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(a - 1)* exp(t), t = 0..x) = GAMMA(a)*(x)^(a)* (- x)^(-(a))*(GAMMA(a)-GAMMA(a, - x))/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Successful [Tested: 9] || Skip - symbolical successful subtest
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.10.E8 8.10.E8] || [[Item:Q2564|<math>\frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\frac{(a+1)(a+2)-x}{(a+1)(a+2+x)} < ax^{-a}e^{-x}I</syntaxhighlight> || <math>x > 0, a \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((a + 1)*(a + 2)- x)/((a + 1)*(a + 2 + x)) < a*(x)^(- a)* exp(- x)*I</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Divide[(a + 1)*(a + 2)- x,(a + 1)*(a + 2 + x)] < a*(x)^(- a)* Exp[- x]*I</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.10#Ex5 8.10#Ex5] || [[Item:Q2565|<math>c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{a} = (\EulerGamma@{1+a})^{1/(a-1)}</syntaxhighlight> || <math>\realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>c[a] = (GAMMA(1 + a))^(1/(a - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, a] == (Gamma[1 + a])^(1/(a - 1))</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9011204630+.5000000000*I
-Test Values: {a = 1.5, c[a] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.267145867+.8660254040*I
-Test Values: {a = 1.5, c[a] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.9011204638598199, 0.49999999999999994]
-Test Values: {Rule[a, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.2671458676442584, 0.8660254037844387]
-Test Values: {Rule[a, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10#Ex6 8.10#Ex6] || [[Item:Q2566|<math>d_{a} = (\EulerGamma@{1+a})^{-1/a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d_{a} = (\EulerGamma@{1+a})^{-1/a}</syntaxhighlight> || <math>\realpart@@{(1+a)} > 0</math> || <syntaxhighlight lang=mathematica>d[a] = (GAMMA(1 + a))^(- 1/a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[d, a] == (Gamma[1 + a])^(- 1/a)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [40 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .388914161e-1+.5000000000*I
-Test Values: {a = 1.5, d[a] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.327133988+.8660254040*I
-Test Values: {a = 1.5, d[a] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [40 / 40]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.038891415918572037, 0.49999999999999994]
-Test Values: {Rule[a, 1.5], Rule[Subscript[d, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.3271339878658663, 0.8660254037844387]
-Test Values: {Rule[a, 1.5], Rule[Subscript[d, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || [[Item:Q2567|<math>\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1\right) < x^{1-a}e^{x}\incGamma@{a}{x}</syntaxhighlight> || <math>x \geq 0, 0 < a, a < 1</math> || <syntaxhighlight lang=mathematica>(x)/(2*a)*((1 +(2)/(x))^(a)- 1) < (x)^(1 - a)* exp(x)*GAMMA(a, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[x,2*a]*((1 +Divide[2,x])^(a)- 1) < (x)^(1 - a)* Exp[x]*Gamma[a, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/8.10.E10 8.10.E10] || [[Item:Q2567|<math>x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x^{1-a}e^{x}\incGamma@{a}{x} \leq \frac{x}{ac_{a}}\left(\left(1+\frac{c_{a}}{x}\right)^{a}-1\right)</syntaxhighlight> || <math>x \geq 0, 0 < a, a < 1</math> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* exp(x)*GAMMA(a, x) <= (x)/(a*c[a])*((1 +(c[a])/(x))^(a)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(x)^(1 - a)* Exp[x]*Gamma[a, x] <= Divide[x,a*Subscript[c, a]]*((1 +Divide[Subscript[c, a],x])^(a)- 1)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8100694499 <= .7912878480
-Test Values: {a = .5, x = 1.5, c[a] = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6556795425 <= .6180339885
-Test Values: {a = .5, x = .5, c[a] = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.8100694501969615, Complex[0.8808481919138387, -0.05137441674828974]]
-Test Values: {Rule[a, 0.5], Rule[x, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[0.8100694501969615, Complex[1.0324243733930456, -0.1801654927820326]]
-Test Values: {Rule[a, 0.5], Rule[x, 1.5], Rule[Subscript[c, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10.E11 8.10.E11] || [[Item:Q2568|<math>(1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(1-e^{-\alpha_{a}x})^{a} \leq \normincGammaP@{a}{x}</syntaxhighlight> || <math>x \geq 0, a > 0</math> || <syntaxhighlight lang=mathematica>(1 - exp(- alpha[a]*x))^(a) <= (GAMMA(a)-GAMMA(a, x))/GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(1 - Exp[- Subscript[\[Alpha], a]*x])^(a) <= GammaRegularized[a, 0, x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [78 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8461432717 <= .6083748237
-Test Values: {a = 1.5, alpha = 1.5, x = 1.5, alpha[a] = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9262567903 <= .6083748237
-Test Values: {a = 1.5, alpha = 1.5, x = 1.5, alpha[a] = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[0.7016331692747775, 0.2500919864059583], 0.608374823728911]
-Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[α, 1.5], Rule[Subscript[α, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[Complex[-1.369574242346028, 2.679891945423719], 0.608374823728911]
-Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[α, 1.5], Rule[Subscript[α, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10.E11 8.10.E11] || [[Item:Q2568|<math>\normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a}{x} \leq (1-e^{-\beta_{a}x})^{a}</syntaxhighlight> || <math>x \geq 0, a > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(a)-GAMMA(a, x))/GAMMA(a) <= (1 - exp(- beta[a]*x))^(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, 0, x] <= (1 - Exp[- Subscript[\[Beta], a]*x])^(a)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6083748237 <= .3832643966
-Test Values: {a = 1.5, beta = 1.5, x = 1.5, beta[a] = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1987480431 <= .1040340193
-Test Values: {a = 1.5, beta = 1.5, x = .5, beta[a] = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [192 / 270]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: LessEqual[0.608374823728911, Complex[0.7016331692747775, 0.2500919864059583]]
-Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[Subscript[β, a], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: LessEqual[0.608374823728911, Complex[-1.369574242346028, 2.679891945423719]]
-Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[β, 1.5], Rule[Subscript[β, a], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.10.E13 8.10.E13] || [[Item:Q2571|<math>\frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\incGamma@{n}{n}}{\EulerGamma@{n}} < \frac{1}{2}</syntaxhighlight> || <math>\realpart@@{n} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(n, n))/(GAMMA(n)) < (1)/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Gamma[n, n],Gamma[n]] < Divide[1,2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/8.10.E13 8.10.E13] || [[Item:Q2571|<math>\frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{2} < \frac{\incGamma@{n}{n-1}}{\EulerGamma@{n}}</syntaxhighlight> || <math>\realpart@@{n} > 0</math> || <syntaxhighlight lang=mathematica>(1)/(2) < (GAMMA(n, n - 1))/(GAMMA(n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2] < Divide[Gamma[n, n - 1],Gamma[n]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/8.11.E2 8.11.E2] || [[Item:Q2573|<math>\incGamma@{a}{z} = z^{a-1}e^{-z}\left(\sum_{k=0}^{n-1}\frac{u_{k}}{z^{k}}+R_{n}(a,z)\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incGamma@{a}{z} = z^{a-1}e^{-z}\left(\sum_{k=0}^{n-1}\frac{u_{k}}{z^{k}}+R_{n}(a,z)\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(a, z) = (z)^(a - 1)* exp(- z)*(sum(((- 1)^(k)* pochhammer(1 - a, k))/((z)^(k)), k = 0..n - 1)+ R[n](a , z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, z] == (z)^(a - 1)* Exp[- z]*(Sum[Divide[(- 1)^(k)* Pochhammer[1 - a, k],(z)^(k)], {k, 0, n - 1}, GenerateConditions->None]+ Subscript[R, n][a , z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1072320848e-1-.1480251451*I+(.9924715785e-1+.4087434498*I)*(1.000000000+0.*I+(.8660254040+.5000000000*I)*(-1.5, .8660254040+.5000000000*I))
-Test Values: {a = -1.5, z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, n = 1, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1072320848e-1-.1480251451*I+(.9924715785e-1+.4087434498*I)*(-1.165063509+1.250000000*I+(.8660254040+.5000000000*I)*(-1.5, .8660254040+.5000000000*I))
-Test Values: {a = -1.5, z = 1/2*3^(1/2)+1/2*I, R[n] = 1/2*3^(1/2)+1/2*I, n = 2, n = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/8.11.E4 8.11.E4] || [[Item:Q2575|<math>\incgamma@{a}{z} = z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Pochhammersym{a}{k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{z} = z^{a}e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Pochhammersym{a}{k+1}}</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, z) = (z)^(a)* exp(- z)*sum(((z)^(k))/(pochhammer(a, k + 1)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, z] == (z)^(a)* Exp[- z]*Sum[Divide[(z)^(k),Pochhammer[a, k + 1]], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.11#Ex1 8.11#Ex1] || [[Item:Q2579|<math>b_{0}(\lambda) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{0}(\lambda) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[0](lambda) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 0][\[Lambda]] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.11#Ex2 8.11#Ex2] || [[Item:Q2580|<math>b_{1}(\lambda) = \lambda</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{1}(\lambda) = \lambda</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[1](lambda) = lambda</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 1][\[Lambda]] == \[Lambda]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.11#Ex3 8.11#Ex3] || [[Item:Q2581|<math>b_{2}(\lambda) = \lambda(2\lambda+1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>b_{2}(\lambda) = \lambda(2\lambda+1)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">b[2](lambda) = lambda*(2*lambda + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[b, 2][\[Lambda]] == \[Lambda]*(2*\[Lambda]+ 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.11.E15 8.11.E15] || [[Item:Q2588|<math>S_{n}(x) = \frac{\incgamma@{n+1}{nx}}{(nx)^{n}e^{-nx}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>S_{n}(x) = \frac{\incgamma@{n+1}{nx}}{(nx)^{n}e^{-nx}}</syntaxhighlight> || <math>\realpart@@{(n+1)} > 0</math> || <syntaxhighlight lang=mathematica>S[n](x) = (GAMMA(n + 1)-GAMMA(n + 1, n*x))/((n*x)^(n)* exp(- n*x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[S, n][x] == Divide[Gamma[n + 1, 0, n*x],(n*x)^(n)* Exp[- n*x]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.22087941e-1+.7500000000*I
-Test Values: {x = 1.5, S[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.275525655+.7500000000*I
-Test Values: {x = 1.5, S[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.02208794121538471, 0.7499999999999999]
-Test Values: {Rule[n, 1], Rule[x, 1.5], Rule[Subscript[S, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.2755256550317124, 0.7499999999999999]
-Test Values: {Rule[n, 2], Rule[x, 1.5], Rule[Subscript[S, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.11.E19 8.11.E19] || [[Item:Q2592|<math>d_{k}(x) = \frac{(-1)^{k}b_{k}(x)}{(1-x)^{2k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>d_{k}(x) = \frac{(-1)^{k}b_{k}(x)}{(1-x)^{2k+1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">d[k](x) = ((- 1)^(k)* b[k](x))/((1 - x)^(2*k + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[d, k][x] == Divide[(- 1)^(k)* Subscript[b, k][x],(1 - x)^(2*k + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex1 8.12#Ex1] || [[Item:Q2593|<math>\lambda = z/a</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda = z/a</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda = z/a</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda] == z/a</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.12#Ex2 8.12#Ex2] || [[Item:Q2594|<math>\eta = \left(2(\lambda-1-\ln@@{\lambda})\right)^{1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\eta = \left(2(\lambda-1-\ln@@{\lambda})\right)^{1/2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>eta = (2*(lambda - 1 - ln(lambda)))^(1/2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Eta] == (2*(\[Lambda]- 1 - Log[\[Lambda]]))^(1/2)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8206105237+1.019626504*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2036159778+2.354396465*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, lambda = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8206105232686428, 1.019626504138681]
-Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.20361597732323333, 2.3543964646926674]
-Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.12#Ex3 8.12#Ex3] || [[Item:Q2595|<math>\tfrac{1}{2}\eta^{2} = \lambda-1-\ln@@{\lambda}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tfrac{1}{2}\eta^{2} = \lambda-1-\ln@@{\lambda}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(2)*(eta)^(2) = lambda - 1 - ln(lambda)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,2]*\[Eta]^(2) == \[Lambda]- 1 - Log[\[Lambda]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3839745964+.4566114775*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.750000000+1.661382400*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, lambda = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.38397459621556135, 0.45661147749051817]
-Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.7499999999999998, 1.6613824005009756]
-Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.12#Ex4 8.12#Ex4] || [[Item:Q2596|<math>\deriv{\eta}{\lambda} = \frac{\lambda-1}{\lambda\eta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{\eta}{\lambda} = \frac{\lambda-1}{\lambda\eta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(eta, lambda) = (lambda - 1)/(lambda*eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[\[Eta], \[Lambda]] == Divide[\[Lambda]- 1,\[Lambda]*\[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.3660254037-.3660254035*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, lambda = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.732050807-.2266367838e-9*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, lambda = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [100 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.3660254037844386, -0.3660254037844386]
-Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.7320508075688772, 3.3306690738754696*^-16]
-Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[λ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.12.E3 8.12.E3] || [[Item:Q2597|<math>\normincGammaP@{a}{z} = \tfrac{1}{2}\erfc@{-\eta\sqrt{a/2}}-S(a,\eta)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaP@{a}{z} = \tfrac{1}{2}\erfc@{-\eta\sqrt{a/2}}-S(a,\eta)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = (1)/(2)*erfc(- eta*sqrt(a/2))- S(a , eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, 0, z] == Divide[1,2]*Erfc[- \[Eta]*Sqrt[a/2]]- S[a , \[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8724483635-.3325384943*I+(.8660254040+.5000000000*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {S = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .8436948583-.7685914925*I+(.8660254040+.5000000000*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {S = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/8.12.E4 8.12.E4] || [[Item:Q2598|<math>\normincGammaQ@{a}{z} = \tfrac{1}{2}\erfc@{\eta\sqrt{a/2}}+S(a,\eta)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaQ@{a}{z} = \tfrac{1}{2}\erfc@{\eta\sqrt{a/2}}+S(a,\eta)</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, z)/GAMMA(a) = (1)/(2)*erfc(eta*sqrt(a/2))+ S(a , eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, z] == Divide[1,2]*Erfc[\[Eta]*Sqrt[a/2]]+ S[a , \[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.8724483631+.3325384943*I-(.8660254040+.5000000000*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {S = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8436948582+.7685914925*I-(.8660254040+.5000000000*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {S = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/8.12.E5 8.12.E5] || [[Item:Q2599|<math>\frac{e^{+\pi ia}}{2i\sin@{\pi a}}\normincGammaQ@{-a}{ze^{+\pi i}} = +\tfrac{1}{2}\erfc@{+ i\eta\sqrt{a/2}}-iT(a,\eta)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{e^{+\pi ia}}{2i\sin@{\pi a}}\normincGammaQ@{-a}{ze^{+\pi i}} = +\tfrac{1}{2}\erfc@{+ i\eta\sqrt{a/2}}-iT(a,\eta)</syntaxhighlight> || <math>\realpart@@{(-a)} > 0</math> || <syntaxhighlight lang=mathematica>(exp(+ Pi*I*a))/(2*I*sin(Pi*a))*GAMMA(- a, z*exp(+ Pi*I))/GAMMA(- a) = +(1)/(2)*erfc(+ I*eta*sqrt(a/2))- I*T(a , eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Exp[+ Pi*I*a],2*I*Sin[Pi*a]]*GammaRegularized[- a, z*Exp[+ Pi*I]] == +Divide[1,2]*Erfc[+ I*\[Eta]*Sqrt[a/2]]- I*T[a , \[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1738836865-.4215091763*I+(-.5000000000+.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5322485765+.1038051776*I+(-.5000000000+.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/8.12.E5 8.12.E5] || [[Item:Q2599|<math>\frac{e^{-\pi ia}}{2i\sin@{\pi a}}\normincGammaQ@{-a}{ze^{-\pi i}} = -\tfrac{1}{2}\erfc@{- i\eta\sqrt{a/2}}-iT(a,\eta)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{e^{-\pi ia}}{2i\sin@{\pi a}}\normincGammaQ@{-a}{ze^{-\pi i}} = -\tfrac{1}{2}\erfc@{- i\eta\sqrt{a/2}}-iT(a,\eta)</syntaxhighlight> || <math>\realpart@@{(-a)} > 0</math> || <syntaxhighlight lang=mathematica>(exp(- Pi*I*a))/(2*I*sin(Pi*a))*GAMMA(- a, z*exp(- Pi*I))/GAMMA(- a) = -(1)/(2)*erfc(- I*eta*sqrt(a/2))- I*T(a , eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Exp[- Pi*I*a],2*I*Sin[Pi*a]]*GammaRegularized[- a, z*Exp[- Pi*I]] == -Divide[1,2]*Erfc[- I*\[Eta]*Sqrt[a/2]]- I*T[a , \[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.9809290254+.1461521622*I+(-.5000000000+.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.2747967621-.3791621909*I+(-.5000000000+.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/8.12#Ex5 8.12#Ex5] || [[Item:Q2600|<math>\EulerGamma@{a+1}\frac{e^{+\pi ia}}{2\pi i}\incGamma@{-a}{ze^{+\pi i}} = -\tfrac{1}{2}\erfc@{+ i\eta\sqrt{a/2}}+iT(a,\eta)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerGamma@{a+1}\frac{e^{+\pi ia}}{2\pi i}\incGamma@{-a}{ze^{+\pi i}} = -\tfrac{1}{2}\erfc@{+ i\eta\sqrt{a/2}}+iT(a,\eta)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(a + 1)*(exp(+ Pi*I*a))/(2*Pi*I)*GAMMA(- a, z*exp(+ Pi*I)) = -(1)/(2)*erfc(+ I*eta*sqrt(a/2))+ I*T(a , eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a + 1]*Divide[Exp[+ Pi*I*a],2*Pi*I]*Gamma[- a, z*Exp[+ Pi*I]] == -Divide[1,2]*Erfc[+ I*\[Eta]*Sqrt[a/2]]+ I*T[a , \[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1738836865+.4215091762*I+(.5000000000-.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5322485766-.1038051776*I+(.5000000000-.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/8.12#Ex5 8.12#Ex5] || [[Item:Q2600|<math>\EulerGamma@{a+1}\frac{e^{-\pi ia}}{2\pi i}\incGamma@{-a}{ze^{-\pi i}} = +\tfrac{1}{2}\erfc@{- i\eta\sqrt{a/2}}+iT(a,\eta)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerGamma@{a+1}\frac{e^{-\pi ia}}{2\pi i}\incGamma@{-a}{ze^{-\pi i}} = +\tfrac{1}{2}\erfc@{- i\eta\sqrt{a/2}}+iT(a,\eta)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>GAMMA(a + 1)*(exp(- Pi*I*a))/(2*Pi*I)*GAMMA(- a, z*exp(- Pi*I)) = +(1)/(2)*erfc(- I*eta*sqrt(a/2))+ I*T(a , eta)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a + 1]*Divide[Exp[- Pi*I*a],2*Pi*I]*Gamma[- a, z*Exp[- Pi*I]] == +Divide[1,2]*Erfc[- I*\[Eta]*Sqrt[a/2]]+ I*T[a , \[Eta]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9809290254-.1461521621*I+(.5000000000-.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2747967620+.3791621907*I+(.5000000000-.8660254040*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Error
-|-
-| [https://dlmf.nist.gov/8.12.E6 8.12.E6] || [[Item:Q2601|<math>z^{-a}\scincgamma@{-a}{-z} = \cos@{\pi a}-2\sin@{\pi a}\left(\frac{e^{\frac{1}{2}a\eta^{2}}}{\sqrt{\pi}}\DawsonsintF@{\eta\sqrt{a/2}}+T(a,\eta)\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{-a}\scincgamma@{-a}{-z} = \cos@{\pi a}-2\sin@{\pi a}\left(\frac{e^{\frac{1}{2}a\eta^{2}}}{\sqrt{\pi}}\DawsonsintF@{\eta\sqrt{a/2}}+T(a,\eta)\right)</syntaxhighlight> || <math>\realpart@@{(-a)} > 0</math> || <syntaxhighlight lang=mathematica>(z)^(- a)* (- z)^(-(- a))*(GAMMA(- a)-GAMMA(- a, - z))/GAMMA(- a) = cos(Pi*a)- 2*sin(Pi*a)*((exp((1)/(2)*a*(eta)^(2)))/(sqrt(Pi))*dawson(eta*sqrt(a/2))+ T(a , eta))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2923043261+1.961858052*I+(1.732050808+1.000000000*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.7583243808+.5495935246*I+(1.732050808+1.000000000*I)*(-1.5, .8660254040+.5000000000*I)
-Test Values: {T = 1/2*3^(1/2)+1/2*I, a = -1.5, eta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex6 8.12#Ex6] || [[Item:Q2604|<math>c_{0}(\eta) = \frac{1}{\mu}-\frac{1}{\eta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{0}(\eta) = \frac{1}{\mu}-\frac{1}{\eta}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[0](eta) = (1)/(mu)-(1)/(eta)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 0][\[Eta]] == Divide[1,\[Mu]]-Divide[1,\[Eta]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex7 8.12#Ex7] || [[Item:Q2605|<math>c_{1}(\eta) = \frac{1}{\eta^{3}}-\frac{1}{\mu^{3}}-\frac{1}{\mu^{2}}-\frac{1}{12\mu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{1}(\eta) = \frac{1}{\eta^{3}}-\frac{1}{\mu^{3}}-\frac{1}{\mu^{2}}-\frac{1}{12\mu}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[1](eta) = (1)/((eta)^(3))-(1)/((mu)^(3))-(1)/((mu)^(2))-(1)/(12*mu)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 1][\[Eta]] == Divide[1,\[Eta]^(3)]-Divide[1,\[Mu]^(3)]-Divide[1,\[Mu]^(2)]-Divide[1,12*\[Mu]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.12.E10 8.12.E10] || [[Item:Q2606|<math>c_{k}(\eta) = \frac{1}{\eta}\deriv{}{\eta}c_{k-1}(\eta)+(-1)^{k}\frac{g_{k}}{\mu}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>c_{k}(\eta) = \frac{1}{\eta}\deriv{}{\eta}c_{k-1}(\eta)+(-1)^{k}\frac{g_{k}}{\mu}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>c[k](eta) = (1)/(eta)*diff(c[k - 1](eta), eta)+(- 1)^(k)*(g[k])/(mu)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[c, k][\[Eta]] == Divide[1,\[Eta]]*D[Subscript[c, k - 1][\[Eta]], \[Eta]]+(- 1)^(k)*Divide[Subscript[g, k],\[Mu]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000004+.8660254040*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, c[k] = 1/2*3^(1/2)+1/2*I, c[k-1] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, k = 1, k = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.500000000+.8660254040*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, mu = 1/2*3^(1/2)+1/2*I, c[k] = 1/2*3^(1/2)+1/2*I, c[k-1] = 1/2*3^(1/2)+1/2*I, g[k] = 1/2*3^(1/2)+1/2*I, k = 2, k = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.5000000000000001, 0.8660254037844386]
-Test Values: {Rule[k, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, Plus[-1, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.5, 0.8660254037844386]
-Test Values: {Rule[k, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, Plus[-1, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[g, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12.E11 8.12.E11] || [[Item:Q2607|<math>c_{k}(\eta) = \sum_{n=0}^{\infty}d_{k,n}\eta^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{k}(\eta) = \sum_{n=0}^{\infty}d_{k,n}\eta^{n}</syntaxhighlight> || <math>|\eta| < 2\sqrt{\pi}</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[k](eta) = sum(d[k , n]*(eta)^(n), n = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, k][\[Eta]] == Sum[Subscript[d, k , n]*\[Eta]^(n), {n, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex8 8.12#Ex8] || [[Item:Q2608|<math>d_{0,n} = (n+2)\alpha_{n+2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>d_{0,n} = (n+2)\alpha_{n+2}</syntaxhighlight> || <math>n \geq 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">d[0 , n] = (n + 2)*alpha[n + 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[d, 0 , n] == (n + 2)*Subscript[\[Alpha], n + 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex9 8.12#Ex9] || [[Item:Q2609|<math>d_{k,n} = (-1)^{k}g_{k}d_{0,n}+(n+2)d_{k-1,n+2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>d_{k,n} = (-1)^{k}g_{k}d_{0,n}+(n+2)d_{k-1,n+2}</syntaxhighlight> || <math>n \geq 0, k \geq 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">d[k , n] = (- 1)^(k)* g[k]*d[0 , n]+(n + 2)*d[k - 1 , n + 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[d, k , n] == (- 1)^(k)* Subscript[g, k]*Subscript[d, 0 , n]+(n + 2)*Subscript[d, k - 1 , n + 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12.E13 8.12.E13] || [[Item:Q2610|<math>\lambda-1 = \eta+\tfrac{1}{3}\eta^{2}+\sum_{n=3}^{\infty}\alpha_{n}\eta^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lambda-1 = \eta+\tfrac{1}{3}\eta^{2}+\sum_{n=3}^{\infty}\alpha_{n}\eta^{n}</syntaxhighlight> || <math>|\eta| < 2\sqrt{\pi}</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">lambda - 1 = eta +(1)/(3)*(eta)^(2)+ sum(alpha[n]*(eta)^(n), n = 3..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Lambda]- 1 == \[Eta]+Divide[1,3]*\[Eta]^(2)+ Sum[Subscript[\[Alpha], n]*\[Eta]^(n), {n, 3, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex10 8.12#Ex10] || [[Item:Q2611|<math>\alpha_{3} = \tfrac{1}{36}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{3} = \tfrac{1}{36}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[3] = (1)/(36)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 3] == Divide[1,36]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex11 8.12#Ex11] || [[Item:Q2612|<math>\alpha_{4} = -\tfrac{1}{270}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{4} = -\tfrac{1}{270}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[4] = -(1)/(270)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 4] == -Divide[1,270]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex12 8.12#Ex12] || [[Item:Q2613|<math>\alpha_{5} = \tfrac{1}{4320}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{5} = \tfrac{1}{4320}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[5] = (1)/(4320)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 5] == Divide[1,4320]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex13 8.12#Ex13] || [[Item:Q2614|<math>\alpha_{6} = \tfrac{1}{17010}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{6} = \tfrac{1}{17010}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[6] = (1)/(17010)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 6] == Divide[1,17010]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex14 8.12#Ex14] || [[Item:Q2615|<math>\alpha_{7} = -\tfrac{139}{54\;43200}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{7} = -\tfrac{139}{54\;43200}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[7] = -(139)/(5443200)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 7] == -Divide[139,5443200]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex15 8.12#Ex15] || [[Item:Q2616|<math>\alpha_{8} = \tfrac{1}{2\;04120}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{8} = \tfrac{1}{2\;04120}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[8] = (1)/(204120)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 8] == Divide[1,204120]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex16 8.12#Ex16] || [[Item:Q2619|<math>c_{0}(0) = -\tfrac{1}{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{0}(0) = -\tfrac{1}{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[0](0) = -(1)/(3)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 0][0] == -Divide[1,3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex17 8.12#Ex17] || [[Item:Q2620|<math>c_{1}(0) = -\tfrac{1}{540}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{1}(0) = -\tfrac{1}{540}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[1](0) = -(1)/(540)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 1][0] == -Divide[1,540]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex18 8.12#Ex18] || [[Item:Q2621|<math>c_{2}(0) = \tfrac{25}{6048}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{2}(0) = \tfrac{25}{6048}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[2](0) = (25)/(6048)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 2][0] == Divide[25,6048]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex19 8.12#Ex19] || [[Item:Q2622|<math>c_{3}(0) = \tfrac{101}{1\;55520}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{3}(0) = \tfrac{101}{1\;55520}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[3](0) = (101)/(155520)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 3][0] == Divide[101,155520]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex20 8.12#Ex20] || [[Item:Q2623|<math>c_{4}(0) = -\tfrac{31\;84811}{36951\;55200}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{4}(0) = -\tfrac{31\;84811}{36951\;55200}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[4](0) = -(3184811)/(3695155200)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 4][0] == -Divide[3184811,3695155200]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.12#Ex21 8.12#Ex21] || [[Item:Q2624|<math>c_{5}(0) = -\tfrac{27\;45493}{81517\;36320}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{5}(0) = -\tfrac{27\;45493}{81517\;36320}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[5](0) = -(2745493)/(8151736320)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 5][0] == -Divide[2745493,8151736320]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.12.E21 8.12.E21] || [[Item:Q2631|<math>\normincGammaQ@{a}{x} = q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincGammaQ@{a}{x} = q</syntaxhighlight> || <math>\realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a, x)/GAMMA(a) = q</syntaxhighlight> || <syntaxhighlight lang=mathematica>GammaRegularized[a, x] == q</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.8512854784-.5000000000*I
-Test Values: {a = -1.5, q = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.5487148961-.5000000000*I
-Test Values: {a = -1.5, q = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.8512854781447857, -0.49999999999999994]
-Test Values: {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.5487148959215247, -0.49999999999999994]
-Test Values: {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.13.E1 8.13.E1] || [[Item:Q2633|<math>x_{-}(a) < \ln@@{|a|}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>x_{-}(a) < \ln@@{|a|}</syntaxhighlight> || <math>-1 < a, a < 0</math> || <syntaxhighlight lang=mathematica>x[-](a) < ln(abs(a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[x, -][a] < Log[Abs[a]]</syntaxhighlight> || Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/8.14.E1 8.14.E1] || [[Item:Q2634|<math>\int_{0}^{\infty}e^{-ax}\frac{\incgamma@{b}{x}}{\EulerGamma@{b}}\diff{x} = \frac{(1+a)^{-b}}{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-ax}\frac{\incgamma@{b}{x}}{\EulerGamma@{b}}\diff{x} = \frac{(1+a)^{-b}}{a}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > -1, \realpart@@{b} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*x)*(GAMMA(b)-GAMMA(b, x))/(GAMMA(b)), x = 0..infinity) = ((1 + a)^(- b))/(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*x]*Divide[Gamma[b, 0, x],Gamma[b]], {x, 0, Infinity}, GenerateConditions->None] == Divide[(1 + a)^(- b),a]</syntaxhighlight> || Successful || Aborted || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.14.E2 8.14.E2] || [[Item:Q2635|<math>\int_{0}^{\infty}e^{-ax}\incGamma@{b}{x}\diff{x} = \EulerGamma@{b}\frac{1-(1+a)^{-b}}{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-ax}\incGamma@{b}{x}\diff{x} = \EulerGamma@{b}\frac{1-(1+a)^{-b}}{a}</syntaxhighlight> || <math>\realpart@@{a} > -1, \realpart@@{b} > -1, \realpart@@{b} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*x)*GAMMA(b, x), x = 0..infinity) = GAMMA(b)*(1 -(1 + a)^(- b))/(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*x]*Gamma[b, x], {x, 0, Infinity}, GenerateConditions->None] == Gamma[b]*Divide[1 -(1 + a)^(- b),a]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 12] || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.14.E3 8.14.E3] || [[Item:Q2636|<math>\int_{0}^{\infty}x^{a-1}\incgamma@{b}{x}\diff{x} = -\frac{\EulerGamma@{a+b}}{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}x^{a-1}\incgamma@{b}{x}\diff{x} = -\frac{\EulerGamma@{a+b}}{a}</syntaxhighlight> || <math>\realpart@@{a} < 0, \realpart@{a+b} > 0, \realpart@@{(a+b)} > 0, \realpart@@{b} > 0</math> || <syntaxhighlight lang=mathematica>int((x)^(a - 1)* GAMMA(b)-GAMMA(b, x), x = 0..infinity) = -(GAMMA(a + b))/(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(x)^(a - 1)* Gamma[b, 0, x], {x, 0, Infinity}, GenerateConditions->None] == -Divide[Gamma[a + b],a]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)
-Test Values: {a = -1.5, b = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)
-Test Values: {a = -.5, b = 1.5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skip - No test values generated
-|-
-| [https://dlmf.nist.gov/8.14.E4 8.14.E4] || [[Item:Q2637|<math>\int_{0}^{\infty}x^{a-1}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}x^{a-1}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@{a+b} > 0, \realpart@@{(a+b)} > 0</math> || <syntaxhighlight lang=mathematica>int((x)^(a - 1)* GAMMA(b, x), x = 0..infinity) = (GAMMA(a + b))/(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(x)^(a - 1)* Gamma[b, x], {x, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[a + b],a]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 12]
-|-
-| [https://dlmf.nist.gov/8.14.E5 8.14.E5] || [[Item:Q2638|<math>\int_{0}^{\infty}x^{a-1}e^{-sx}\incgamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{b(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+b}{1/(1+s)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}x^{a-1}e^{-sx}\incgamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{b(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+b}{1/(1+s)}</syntaxhighlight> || <math>\realpart@@{s} > 0, \realpart@{a+b} > 0, \realpart@@{(a+b)} > 0, \realpart@@{b} > 0</math> || <syntaxhighlight lang=mathematica>int((x)^(a - 1)* exp(- s*x)*GAMMA(b)-GAMMA(b, x), x = 0..infinity) = (GAMMA(a + b))/(b*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + b], 1/(1 + s))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, 0, x], {x, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[a + b],b*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + b, 1/(1 + s)]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 36]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)
-Test Values: {a = -1.5, b = 2, s = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)
-Test Values: {a = -1.5, b = 2, s = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.14.E6 8.14.E6] || [[Item:Q2639|<math>\int_{0}^{\infty}x^{a-1}e^{-sx}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+a}{s/(1+s)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}x^{a-1}e^{-sx}\incGamma@{b}{x}\diff{x} = \frac{\EulerGamma@{a+b}}{a(1+s)^{a+b}}\*\hyperF@{1}{a+b}{1+a}{s/(1+s)}</syntaxhighlight> || <math>\realpart@@{s} > -1, \realpart@{a+b} > 0, \realpart@@{a} > 0, \realpart@@{(a+b)} > 0</math> || <syntaxhighlight lang=mathematica>int((x)^(a - 1)* exp(- s*x)*GAMMA(b, x), x = 0..infinity) = (GAMMA(a + b))/(a*(1 + s)^(a + b))* hypergeom([1, a + b], [1 + a], s/(1 + s))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(x)^(a - 1)* Exp[- s*x]*Gamma[b, x], {x, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[a + b],a*(1 + s)^(a + b)]* Hypergeometric2F1[1, a + b, 1 + a, s/(1 + s)]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.15.E1 8.15.E1] || [[Item:Q2640|<math>\incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incgamma@{a}{\lambda x} = \lambda^{a}\sum_{k=0}^{\infty}\incgamma@{a+k}{x}\frac{(1-\lambda)^{k}}{k!}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a+k)} > 0</math> || <syntaxhighlight lang=mathematica>GAMMA(a)-GAMMA(a, lambda*x) = (lambda)^(a)* sum(GAMMA(a + k)-GAMMA(a + k, x)*((1 - lambda)^(k))/(factorial(k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Gamma[a, 0, \[Lambda]*x] == \[Lambda]^(a)* Sum[Gamma[a + k, 0, x]*Divide[(1 - \[Lambda])^(k),(k)!], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [90 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(infinity)+Float(infinity)*I
-Test Values: {a = 1.5, lambda = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.17.E1 8.17.E1] || [[Item:Q2641|<math>\incBeta{x}@{a}{b} = \int_{0}^{x}t^{a-1}(1-t)^{b-1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incBeta{x}@{a}{b} = \int_{0}^{x}t^{a-1}(1-t)^{b-1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x) = int((t)^(a - 1)*(1 - t)^(b - 1), t = 0..x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Beta[x, a, b] == Integrate[(t)^(a - 1)*(1 - t)^(b - 1), {t, 0, x}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 108]
-|-
-| [https://dlmf.nist.gov/8.17.E2 8.17.E2] || [[Item:Q2642|<math>\normincBetaI{x}@{a}{b} = \incBeta{x}@{a}{b}/\EulerBeta@{a}{b}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = \incBeta{x}@{a}{b}/\EulerBeta@{a}{b}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == Beta[x, a, b]/Beta[a, b]</syntaxhighlight> || Missing Macro Error || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [45 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E3 8.17.E3] || [[Item:Q2643|<math>\EulerBeta@{a}{b} = \frac{\EulerGamma@{a}\EulerGamma@{b}}{\EulerGamma@{a+b}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerBeta@{a}{b} = \frac{\EulerGamma@{a}\EulerGamma@{b}}{\EulerGamma@{a+b}}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0</math> || <syntaxhighlight lang=mathematica>Beta(a, b) = (GAMMA(a)*GAMMA(b))/(GAMMA(a + b))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Beta[a, b] == Divide[Gamma[a]*Gamma[b],Gamma[a + b]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 9] || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.17.E4 8.17.E4] || [[Item:Q2644|<math>\normincBetaI{x}@{a}{b} = 1-\normincBetaI{1-x}@{b}{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = 1-\normincBetaI{1-x}@{b}{a}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0, \realpart@@{(b+b)} > 0, \realpart@@{(a+a)} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == 1 - BetaRegularized[1 - x, b, a]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E5 8.17.E5] || [[Item:Q2645|<math>\normincBetaI{x}@{m}{n-m+1} = \sum_{j=m}^{n}\binom{n}{j}x^{j}(1-x)^{n-j}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{m}{n-m+1} = \sum_{j=m}^{n}\binom{n}{j}x^{j}(1-x)^{n-j}</syntaxhighlight> || <math>0 \leq x, x < 1, \realpart@@{m} > 0, \realpart@@{(n-m+1)} > 0, \realpart@@{(m+b)} > 0, \realpart@@{(a+(n-m+1))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, m, n - m + 1] == Sum[Binomial[n,j]*(x)^(j)*(1 - x)^(n - j), {j, m, n}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.17.E6 8.17.E6] || [[Item:Q2646|<math>\normincBetaI{x}@{a}{a} = \tfrac{1}{2}\normincBetaI{4x(1-x)}@{a}{\tfrac{1}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{a} = \tfrac{1}{2}\normincBetaI{4x(1-x)}@{a}{\tfrac{1}{2}}</syntaxhighlight> || <math>0 \leq x, x \leq \frac{1}{2}, \realpart@@{a} > 0, \realpart@@{(\tfrac{1}{2})} > 0, \realpart@@{(a+b)} > 0, \realpart@@{(a+a)} > 0, \realpart@@{(a+(\tfrac{1}{2}))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, a] == Divide[1,2]*BetaRegularized[4*x*(1 - x), a, Divide[1,2]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 6]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[x, 0.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -0.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E7 8.17.E7] || [[Item:Q2647|<math>\incBeta{x}@{a}{b} = \frac{x^{a}}{a}\hyperF@{a}{1-b}{a+1}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incBeta{x}@{a}{b} = \frac{x^{a}}{a}\hyperF@{a}{1-b}{a+1}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x) = ((x)^(a))/(a)*hypergeom([a, 1 - b], [a + 1], x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Beta[x, a, b] == Divide[(x)^(a),a]*Hypergeometric2F1[a, 1 - b, a + 1, x]</syntaxhighlight> || Failure || Successful || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[b, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[b, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E8 8.17.E8] || [[Item:Q2648|<math>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{a}\hyperF@{a+b}{1}{a+1}{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{a}\hyperF@{a+b}{1}{a+1}{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x) = ((x)^(a)*(1 - x)^(b))/(a)*hypergeom([a + b, 1], [a + 1], x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Beta[x, a, b] == Divide[(x)^(a)*(1 - x)^(b),a]*Hypergeometric2F1[a + b, 1, a + 1, x]</syntaxhighlight> || Failure || Successful || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[b, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -2], Rule[b, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E9 8.17.E9] || [[Item:Q2649|<math>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b-1}}{a}\hyperF@@{1}{1-b}{a+1}{\frac{x}{x-1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\incBeta{x}@{a}{b} = \frac{x^{a}(1-x)^{b-1}}{a}\hyperF@@{1}{1-b}{a+1}{\frac{x}{x-1}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>int(t^(a-1)*(1-t)^(b-1), t = 0 .. x) = ((x)^(a)*(1 - x)^(b - 1))/(a)*hypergeom([1, 1 - b], [a + 1], (x)/(x - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Beta[x, a, b] == Divide[(x)^(a)*(1 - x)^(b - 1),a]*Hypergeometric2F1[1, 1 - b, a + 1, Divide[x,x - 1]]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [46 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[4.9960036108132044*^-15, -27.48893571891068]
-Test Values: {Rule[a, -1.5], Rule[b, -2], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[3.191891195797325*^-15, -27.48893571891068]
-Test Values: {Rule[a, -1.5], Rule[b, -2], Rule[x, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E10 8.17.E10] || [[Item:Q2650|<math>\normincBetaI{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{2\pi i}\int_{c-i\infty}^{c+i\infty}s^{-a}(1-s)^{-b}\frac{\diff{s}}{s-x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = \frac{x^{a}(1-x)^{b}}{2\pi i}\int_{c-i\infty}^{c+i\infty}s^{-a}(1-s)^{-b}\frac{\diff{s}}{s-x}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == Divide[(x)^(a)*(1 - x)^(b),2*Pi*I]*Integrate[(s)^(- a)*(1 - s)^(- b)*Divide[1,s - x], {s, c - I*Infinity, c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.17.E12 8.17.E12] || [[Item:Q2653|<math>\normincBetaI{x}@{a}{b} = x\normincBetaI{x}@{a-1}{b}+x^{\prime}\normincBetaI{x}@{a}{b-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = x\normincBetaI{x}@{a-1}{b}+x^{\prime}\normincBetaI{x}@{a}{b-1}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a-1)} > 0, \realpart@@{b} > 0, \realpart@@{(b-1)} > 0, \realpart@@{(a+b)} > 0, \realpart@@{((a-1)+b)} > 0, \realpart@@{(a+(b-1))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == x*BetaRegularized[x, a - 1, b]+(1 - x)*BetaRegularized[x, a, b - 1]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/8.17.E13 8.17.E13] || [[Item:Q2654|<math>(a+b)\normincBetaI{x}@{a}{b} = a\normincBetaI{x}@{a+1}{b}+b\normincBetaI{x}@{a}{b+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(a+b)\normincBetaI{x}@{a}{b} = a\normincBetaI{x}@{a+1}{b}+b\normincBetaI{x}@{a}{b+1}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a+1)} > 0, \realpart@@{b} > 0, \realpart@@{(b+1)} > 0, \realpart@@{(a+b)} > 0, \realpart@@{((a+1)+b)} > 0, \realpart@@{(a+(b+1))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(a + b)*BetaRegularized[x, a, b] == a*BetaRegularized[x, a + 1, b]+ b*BetaRegularized[x, a, b + 1]</syntaxhighlight> || Missing Macro Error || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [33 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E14 8.17.E14] || [[Item:Q2655|<math>(a+bx)\normincBetaI{x}@{a}{b} = xb\normincBetaI{x}@{a-1}{b+1}+a\normincBetaI{x}@{a+1}{b}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(a+bx)\normincBetaI{x}@{a}{b} = xb\normincBetaI{x}@{a-1}{b+1}+a\normincBetaI{x}@{a+1}{b}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{(a-1)} > 0, \realpart@@{(a+1)} > 0, \realpart@@{b} > 0, \realpart@@{(b+1)} > 0, \realpart@@{(a+b)} > 0, \realpart@@{((a-1)+b)} > 0, \realpart@@{((a+1)+b)} > 0, \realpart@@{(a+(b+1))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(a + b*x)*BetaRegularized[x, a, b] == x*b*BetaRegularized[x, a - 1, b + 1]+ a*BetaRegularized[x, a + 1, b]</syntaxhighlight> || Missing Macro Error || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [36 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E16 8.17.E16] || [[Item:Q2657|<math>a\normincBetaI{x}@{a+1}{b} = (a+cx)\normincBetaI{x}@{a}{b}-cx\normincBetaI{x}@{a-1}{b}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>a\normincBetaI{x}@{a+1}{b} = (a+cx)\normincBetaI{x}@{a}{b}-cx\normincBetaI{x}@{a-1}{b}</syntaxhighlight> || <math>\realpart@@{(a+1)} > 0, \realpart@@{a} > 0, \realpart@@{(a-1)} > 0, \realpart@@{b} > 0, \realpart@@{((a+1)+b)} > 0, \realpart@@{(a+b)} > 0, \realpart@@{((a-1)+b)} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>a*BetaRegularized[x, a + 1, b] == (a + c*x)*BetaRegularized[x, a, b]- c*x*BetaRegularized[x, a - 1, b]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.17.E18 8.17.E18] || [[Item:Q2659|<math>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a+1}{b-1}+\frac{x^{a}(x^{\prime})^{b-1}}{a\EulerBeta@{a}{b}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a+1}{b-1}+\frac{x^{a}(x^{\prime})^{b-1}}{a\EulerBeta@{a}{b}}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0, \realpart@@{(a+1)} > 0, \realpart@@{(b-1)} > 0, \realpart@@{((a+1)+b)} > 0, \realpart@@{(a+(b-1))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == BetaRegularized[x, a + 1, b - 1]+Divide[(x)^(a)*((1 - x))^(b - 1),a*Beta[a, b]]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/8.17.E19 8.17.E19] || [[Item:Q2660|<math>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a-1}{b+1}-\frac{x^{a-1}(x^{\prime})^{b}}{b\EulerBeta@{a}{b}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a-1}{b+1}-\frac{x^{a-1}(x^{\prime})^{b}}{b\EulerBeta@{a}{b}}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0, \realpart@@{(a-1)} > 0, \realpart@@{(b+1)} > 0, \realpart@@{((a-1)+b)} > 0, \realpart@@{(a+(b+1))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == BetaRegularized[x, a - 1, b + 1]-Divide[(x)^(a - 1)*((1 - x))^(b),b*Beta[a, b]]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/8.17.E20 8.17.E20] || [[Item:Q2661|<math>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a+1}{b}+\frac{x^{a}(x^{\prime})^{b}}{a\EulerBeta@{a}{b}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a+1}{b}+\frac{x^{a}(x^{\prime})^{b}}{a\EulerBeta@{a}{b}}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0, \realpart@@{(a+1)} > 0, \realpart@@{((a+1)+b)} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == BetaRegularized[x, a + 1, b]+Divide[(x)^(a)*((1 - x))^(b),a*Beta[a, b]]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
-|-
-| [https://dlmf.nist.gov/8.17.E21 8.17.E21] || [[Item:Q2662|<math>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a}{b+1}-\frac{x^{a}(x^{\prime})^{b}}{b\EulerBeta@{a}{b}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = \normincBetaI{x}@{a}{b+1}-\frac{x^{a}(x^{\prime})^{b}}{b\EulerBeta@{a}{b}}</syntaxhighlight> || <math>\realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0, \realpart@@{(b+1)} > 0, \realpart@@{(a+(b+1))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == BetaRegularized[x, a, b + 1]-Divide[(x)^(a)*((1 - x))^(b),b*Beta[a, b]]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.17#Ex3 8.17#Ex3] || [[Item:Q2664|<math>d_{2m} = \frac{m(b-m)x}{(a+2m-1)(a+2m)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>d_{2m} = \frac{m(b-m)x}{(a+2m-1)(a+2m)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">d[2*m] = (m*(b - m)*x)/((a + 2*m - 1)*(a + 2*m))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[d, 2*m] == Divide[m*(b - m)*x,(a + 2*m - 1)*(a + 2*m)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.17#Ex4 8.17#Ex4] || [[Item:Q2665|<math>d_{2m+1} = -\frac{(a+m)(a+b+m)x}{(a+2m)(a+2m+1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>d_{2m+1} = -\frac{(a+m)(a+b+m)x}{(a+2m)(a+2m+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">d[2*m + 1] = -((a + m)*(a + b + m)*x)/((a + 2*m)*(a + 2*m + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[d, 2*m + 1] == -Divide[(a + m)*(a + b + m)*x,(a + 2*m)*(a + 2*m + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.17.E24 8.17.E24] || [[Item:Q2666|<math>\normincBetaI{x}@{m}{n} = (1-x)^{n}\sum_{j=m}^{\infty}\binom{n+j-1}{j}x^{j}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{m}{n} = (1-x)^{n}\sum_{j=m}^{\infty}\binom{n+j-1}{j}x^{j}</syntaxhighlight> || <math>0 \leq x, x < 1, \realpart@@{m} > 0, \realpart@@{n} > 0, \realpart@@{(m+b)} > 0, \realpart@@{(a+n)} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, m, n] == (1 - x)^(n)* Sum[Binomial[n + j - 1,j]*(x)^(j), {j, m, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.18.E2 8.18.E2] || [[Item:Q2668|<math>\xi = -\ln@@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\xi = -\ln@@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>xi = - ln(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Xi] == - Log[x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.271490512+.5000000000*I
-Test Values: {x = 1.5, xi = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.945348919e-1+.8660254040*I
-Test Values: {x = 1.5, xi = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.271490511892603, 0.49999999999999994]
-Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.0945348918918354, 0.8660254037844387]
-Test Values: {Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18.E4 8.18.E4] || [[Item:Q2670|<math>aF_{k+1} = (k+b-a\xi)F_{k}+k\xi F_{k-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>aF_{k+1} = (k+b-a\xi)F_{k}+k\xi F_{k-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a*F[k + 1] = (k + b - a*xi)*F[k]+ k*xi*F[k - 1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a*Subscript[F, k + 1] == (k + b - a*\[Xi])*Subscript[F, k]+ k*\[Xi]*Subscript[F, k - 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.18#Ex1 8.18#Ex1] || [[Item:Q2671|<math>F_{0} = a^{-b}\normincGammaQ@{b}{a\xi}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>F_{0} = a^{-b}\normincGammaQ@{b}{a\xi}</syntaxhighlight> || <math>\realpart@@{b} > 0</math> || <syntaxhighlight lang=mathematica>F[0] = (a)^(- b)* GAMMA(b, a*xi)/GAMMA(b)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[F, 0] == (a)^(- b)* GammaRegularized[b, a*\[Xi]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.253924788+1.407498490*I
-Test Values: {a = -1.5, b = -1.5, xi = 1/2*3^(1/2)+1/2*I, F[0] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.1121006157+1.773523894*I
-Test Values: {a = -1.5, b = -1.5, xi = 1/2*3^(1/2)+1/2*I, F[0] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.2539247882576399, 1.4074984905445393]
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[F, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.11210061552679867, 1.7735238943289782]
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[F, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.18#Ex2 8.18#Ex2] || [[Item:Q2672|<math>F_{1} = \frac{b-a\xi}{a}F_{0}+\frac{\xi^{b}e^{-a\xi}}{a\EulerGamma@{b}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>F_{1} = \frac{b-a\xi}{a}F_{0}+\frac{\xi^{b}e^{-a\xi}}{a\EulerGamma@{b}}</syntaxhighlight> || <math>\realpart@@{b} > 0</math> || <syntaxhighlight lang=mathematica>F[1] = (b - a*xi)/(a)*F[0]+((xi)^(b)* exp(- a*xi))/(a*GAMMA(b))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[F, 1] == Divide[b - a*\[Xi],a]*Subscript[F, 0]+Divide[\[Xi]^(b)* Exp[- a*\[Xi]],a*Gamma[b]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.329643864+4.621882749*I
-Test Values: {a = -1.5, b = 1.5, xi = 1/2*3^(1/2)+1/2*I, F[0] = 1/2*3^(1/2)+1/2*I, F[1] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9636184598+4.987908153*I
-Test Values: {a = -1.5, b = 1.5, xi = 1/2*3^(1/2)+1/2*I, F[0] = 1/2*3^(1/2)+1/2*I, F[1] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[2.32964386182885, 4.621882746395113]
-Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[F, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[F, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.9636184580444114, 4.9879081501795515]
-Test Values: {Rule[a, -1.5], Rule[b, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[F, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[F, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18.E6 8.18.E6] || [[Item:Q2673|<math>\left(\frac{1-e^{-t}}{t}\right)^{b-1} = \sum_{k=0}^{\infty}d_{k}(t-\xi)^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\left(\frac{1-e^{-t}}{t}\right)^{b-1} = \sum_{k=0}^{\infty}d_{k}(t-\xi)^{k}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((1 - exp(- t))/(t))^(b - 1) = sum(d[k]*(t - xi)^(k), k = 0..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Divide[1 - Exp[- t],t])^(b - 1) == Sum[Subscript[d, k]*(t - \[Xi])^(k), {k, 0, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18#Ex3 8.18#Ex3] || [[Item:Q2674|<math>d_{0} = \left(\frac{1-x}{\xi}\right)^{b-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>d_{0} = \left(\frac{1-x}{\xi}\right)^{b-1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">d[0] = ((1 - x)/(xi))^(b - 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[d, 0] == (Divide[1 - x,\[Xi]])^(b - 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18#Ex4 8.18#Ex4] || [[Item:Q2675|<math>d_{1} = \frac{x\xi+x-1}{(1-x)\xi}(b-1)d_{0}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>d_{1} = \frac{x\xi+x-1}{(1-x)\xi}(b-1)d_{0}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">d[1] = (x*xi + x - 1)/((1 - x)*xi)*(b - 1)*d[0]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[d, 1] == Divide[x*\[Xi]+ x - 1,(1 - x)*\[Xi]]*(b - 1)*Subscript[d, 0]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18.E8 8.18.E8] || [[Item:Q2676|<math>x_{0} = a/(a+b)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{0} = a/(a+b)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[0] = a/(a + b)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, 0] == a/(a + b)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.18.E10 8.18.E10] || [[Item:Q2678|<math>-\tfrac{1}{2}\eta^{2} = x_{0}\ln@{\frac{x}{x_{0}}}+(1-x_{0})\ln@{\frac{1-x}{1-x_{0}}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\tfrac{1}{2}\eta^{2} = x_{0}\ln@{\frac{x}{x_{0}}}+(1-x_{0})\ln@{\frac{1-x}{1-x_{0}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-(1)/(2)*(eta)^(2) = x[0]*ln((x)/(x[0]))+(1 - x[0])*ln((1 - x)/(1 - x[0]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[1,2]*\[Eta]^(2) == Subscript[x, 0]*Log[Divide[x,Subscript[x, 0]]]+(1 - Subscript[x, 0])*Log[Divide[1 - x,1 - Subscript[x, 0]]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .580000474e-1+.458917392e-1*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 1.5, x[0] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.269862383+1.019641337*I
-Test Values: {eta = 1/2*3^(1/2)+1/2*I, x = 1.5, x[0] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.058000047924774145, 0.04589173995258988]
-Test Values: {Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.2698623824536366, 1.0196413375539057]
-Test Values: {Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18.E11 8.18.E11] || [[Item:Q2679|<math>c_{0}(\eta) = \frac{1}{\eta}-\frac{\sqrt{x_{0}(1-x_{0})}}{x-x_{0}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{0}(\eta) = \frac{1}{\eta}-\frac{\sqrt{x_{0}(1-x_{0})}}{x-x_{0}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[0](eta) = (1)/(eta)-(sqrt(x[0]*(1 - x[0])))/(x - x[0])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 0][\[Eta]] == Divide[1,\[Eta]]-Divide[Sqrt[Subscript[x, 0]*(1 - Subscript[x, 0])],x - Subscript[x, 0]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18.E12 8.18.E12] || [[Item:Q2680|<math>c_{0}(0) = \frac{1-2x_{0}}{3\sqrt{x_{0}(1-x_{0})}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{0}(0) = \frac{1-2x_{0}}{3\sqrt{x_{0}(1-x_{0})}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[0](0) = (1 - 2*x[0])/(3*sqrt(x[0]*(1 - x[0])))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, 0][0] == Divide[1 - 2*Subscript[x, 0],3*Sqrt[Subscript[x, 0]*(1 - Subscript[x, 0])]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.18.E15 8.18.E15] || [[Item:Q2683|<math>\mu\ln@@{\zeta}-\zeta = \ln@@{x}+\mu\ln@{1-x}+(1+\mu)\ln@{1+\mu}-\mu</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\mu\ln@@{\zeta}-\zeta = \ln@@{x}+\mu\ln@{1-x}+(1+\mu)\ln@{1+\mu}-\mu</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>mu*ln(zeta)- zeta = ln(x)+ mu*ln(1 - x)+(1 + mu)*ln(1 + mu)- mu</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Mu]*Log[\[Zeta]]- \[Zeta] == Log[x]+ \[Mu]*Log[1 - x]+(1 + \[Mu])*Log[1 + \[Mu]]- \[Mu]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .405976146-2.738439399*I
-Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 1.5, zeta = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9866033870-1.744115280*I
-Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 1.5, zeta = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [299 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.4059761460255107, -2.7384393975724306]
-Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.0560847852373059, 1.7517066341083583]
-Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18.E16 8.18.E16] || [[Item:Q2684|<math>h_{0}(\zeta,\mu) = \mu\left(\frac{1}{\zeta-\mu}-\frac{(1+\mu)^{-3/2}}{x_{0}-x}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>h_{0}(\zeta,\mu) = \mu\left(\frac{1}{\zeta-\mu}-\frac{(1+\mu)^{-3/2}}{x_{0}-x}\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">h[0](zeta , mu) = mu*((1)/(zeta - mu)-((1 + mu)^(- 3/2))/(x[0]- x))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[h, 0][\[Zeta], \[Mu]] == \[Mu]*(Divide[1,\[Zeta]- \[Mu]]-Divide[(1 + \[Mu])^(- 3/2),Subscript[x, 0]- x])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.18.E17 8.18.E17] || [[Item:Q2685|<math>h_{0}(\mu,\mu) = \frac{1}{3}\left(\frac{1-\mu}{\sqrt{1+\mu}}-1\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>h_{0}(\mu,\mu) = \frac{1}{3}\left(\frac{1-\mu}{\sqrt{1+\mu}}-1\right)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">h[0](mu , mu) = (1)/(3)*((1 - mu)/(sqrt(1 + mu))- 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[h, 0][\[Mu], \[Mu]] == Divide[1,3]*(Divide[1 - \[Mu],Sqrt[1 + \[Mu]]]- 1)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.18.E18 8.18.E18] || [[Item:Q2686|<math>\normincBetaI{x}@{a}{b} = p</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\normincBetaI{x}@{a}{b} = p</syntaxhighlight> || <math>0 \leq p, p \leq 1, \realpart@@{a} > 0, \realpart@@{b} > 0, \realpart@@{(a+b)} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>BetaRegularized[x, a, b] == p</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [105 / 108]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: DirectedInfinity[]
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[p, 0.5], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[p, 0.5], Rule[x, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.19.E1 8.19.E1] || [[Item:Q2687|<math>\genexpintE{p}@{z} = z^{p-1}\incGamma@{1-p}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = z^{p-1}\incGamma@{1-p}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(p, z) = (z)^(p - 1)* GAMMA(1 - p, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == (z)^(p - 1)* Gamma[1 - p, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/8.19.E2 8.19.E2] || [[Item:Q2688|<math>\genexpintE{p}@{z} = z^{p-1}\int_{z}^{\infty}\frac{e^{-t}}{t^{p}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = z^{p-1}\int_{z}^{\infty}\frac{e^{-t}}{t^{p}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(p, z) = (z)^(p - 1)* int((exp(- t))/((t)^(p)), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == (z)^(p - 1)* Integrate[Divide[Exp[- t],(t)^(p)], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/8.19.E3 8.19.E3] || [[Item:Q2689|<math>\genexpintE{p}@{z} = \int_{1}^{\infty}\frac{e^{-zt}}{t^{p}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = \int_{1}^{\infty}\frac{e^{-zt}}{t^{p}}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi</math> || <syntaxhighlight lang=mathematica>Ei(p, z) = int((exp(- z*t))/((t)^(p)), t = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == Integrate[Divide[Exp[- z*t],(t)^(p)], {t, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 50]
-|-
-| [https://dlmf.nist.gov/8.19.E4 8.19.E4] || [[Item:Q2690|<math>\genexpintE{p}@{z} = \frac{z^{p-1}e^{-z}}{\EulerGamma@{p}}\int_{0}^{\infty}\frac{t^{p-1}e^{-zt}}{1+t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = \frac{z^{p-1}e^{-z}}{\EulerGamma@{p}}\int_{0}^{\infty}\frac{t^{p-1}e^{-zt}}{1+t}\diff{t}</syntaxhighlight> || <math>|\phase@@{z}| < \tfrac{1}{2}\pi, \realpart@@{p} > 0</math> || <syntaxhighlight lang=mathematica>Ei(p, z) = ((z)^(p - 1)* exp(- z))/(GAMMA(p))*int(((t)^(p - 1)* exp(- z*t))/(1 + t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == Divide[(z)^(p - 1)* Exp[- z],Gamma[p]]*Integrate[Divide[(t)^(p - 1)* Exp[- z*t],1 + t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 25]
-|-
-| [https://dlmf.nist.gov/8.19.E5 8.19.E5] || [[Item:Q2691|<math>\genexpintE{0}@{z} = z^{-1}e^{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{0}@{z} = z^{-1}e^{-z}</syntaxhighlight> || <math>z \neq 0</math> || <syntaxhighlight lang=mathematica>Ei(0, z) = (z)^(- 1)* exp(- z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[0, z] == (z)^(- 1)* Exp[- z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
-|-
-| [https://dlmf.nist.gov/8.19.E6 8.19.E6] || [[Item:Q2692|<math>\genexpintE{p}@{0} = \frac{1}{p-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{0} = \frac{1}{p-1}</syntaxhighlight> || <math>\realpart@@{p} > 1</math> || <syntaxhighlight lang=mathematica>Ei(p, 0) = (1)/(p - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, 0] == Divide[1,p - 1]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 2]
-|-
-| [https://dlmf.nist.gov/8.19.E7 8.19.E7] || [[Item:Q2693|<math>\genexpintE{n}@{z} = \frac{(-z)^{n-1}}{(n-1)!}\expintE@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=0}^{n-2}(n-k-2)!(-z)^{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{n}@{z} = \frac{(-z)^{n-1}}{(n-1)!}\expintE@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=0}^{n-2}(n-k-2)!(-z)^{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(n, z) = ((- z)^(n - 1))/(factorial(n - 1))*Ei(z)+(exp(- z))/(factorial(n - 1))*sum(factorial(n - k - 2)*(- z)^(k), k = 0..n - 2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[n, z] == Divide[(- z)^(n - 1),(n - 1)!]*ExpIntegralE[1, z]+Divide[Exp[- z],(n - 1)!]*Sum[(n - k - 2)!*(- z)^(k), {k, 0, n - 2}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [21 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.393548628-1.498247032*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, n = 1, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4577249979+1.994294304*I
-Test Values: {z = 1/2*3^(1/2)+1/2*I, n = 2, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Successful [Tested: 21]
-|-
-| [https://dlmf.nist.gov/8.19.E9 8.19.E9] || [[Item:Q2695|<math>\genexpintE{n}@{z} = \frac{(-1)^{n}z^{n-1}}{(n-1)!}\ln@@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=1}^{n-1}(-z)^{k-1}\EulerGamma@{n-k}+\frac{e^{-z}(-z)^{n-1}}{(n-1)!}\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\digamma@{k+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{n}@{z} = \frac{(-1)^{n}z^{n-1}}{(n-1)!}\ln@@{z}+\frac{e^{-z}}{(n-1)!}\sum_{k=1}^{n-1}(-z)^{k-1}\EulerGamma@{n-k}+\frac{e^{-z}(-z)^{n-1}}{(n-1)!}\sum_{k=0}^{\infty}\frac{z^{k}}{k!}\digamma@{k+1}</syntaxhighlight> || <math>\realpart@@{(n-k)} > 0</math> || <syntaxhighlight lang=mathematica>Ei(n, z) = ((- 1)^(n)* (z)^(n - 1))/(factorial(n - 1))*ln(z)+(exp(- z))/(factorial(n - 1))*sum((- z)^(k - 1)* GAMMA(n - k), k = 1..n - 1)+(exp(- z)*(- z)^(n - 1))/(factorial(n - 1))*sum(((z)^(k))/(factorial(k))*Psi(k + 1), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[n, z] == Divide[(- 1)^(n)* (z)^(n - 1),(n - 1)!]*Log[z]+Divide[Exp[- z],(n - 1)!]*Sum[(- z)^(k - 1)* Gamma[n - k], {k, 1, n - 1}, GenerateConditions->None]+Divide[Exp[- z]*(- z)^(n - 1),(n - 1)!]*Sum[Divide[(z)^(k),(k)!]*PolyGamma[k + 1], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || <div class="toccolours mw-collapsible mw-collapsed">Failed [16 / 21]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.3691288000469654, -0.2016559825387078], Times[Complex[0.2188469268397846, -0.35920360372711485], Plus[-1.0, DifferenceRoot[Function[{, }
-Test Values: {Equal[Plus[Times[Power[-1, Rational[1, 6]], []], Times[Plus[1, Times[-1, Power[-1, Rational[1, 6]]], Times[-1, ]], [Plus[1, ]]], Times[Plus[-1, ], [Plus[2, ]]]], 0], Equal[[0], 0], Equal[[1], 1]}]][2.0]]]], {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-0.0256870546657635, -0.10579058942927923], Times[Complex[0.1094234634198923, -0.17960180186355743], Plus[-2.0, DifferenceRoot[Function[{, }
-Test Values: {Equal[Plus[Times[Power[-1, Rational[1, 6]], []], Times[Plus[2, Times[-1, Power[-1, Rational[1, 6]]], Times[-1, ]], [Plus[1, ]]], Times[Plus[-2, ], [Plus[2, ]]]], 0], Equal[[0], 0], Equal[[1], 2]}]][3.0]]]], {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.19.E10 8.19.E10] || [[Item:Q2696|<math>\genexpintE{p}@{z} = z^{p-1}\EulerGamma@{1-p}-\sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(1-p+k)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = z^{p-1}\EulerGamma@{1-p}-\sum_{k=0}^{\infty}\frac{(-z)^{k}}{k!(1-p+k)}</syntaxhighlight> || <math>\realpart@@{(1-p)} > 0</math> || <syntaxhighlight lang=mathematica>Ei(p, z) = (z)^(p - 1)* GAMMA(1 - p)- sum(((- z)^(k))/(factorial(k)*(1 - p + k)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == (z)^(p - 1)* Gamma[1 - p]- Sum[Divide[(- z)^(k),(k)!*(1 - p + k)], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 56]
-|-
-| [https://dlmf.nist.gov/8.19.E11 8.19.E11] || [[Item:Q2697|<math>\genexpintE{p}@{z} = \EulerGamma@{1-p}\left(z^{p-1}-e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{2-p+k}}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = \EulerGamma@{1-p}\left(z^{p-1}-e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\EulerGamma@{2-p+k}}\right)</syntaxhighlight> || <math>\realpart@@{(1-p)} > 0, \realpart@@{(2-p+k)} > 0</math> || <syntaxhighlight lang=mathematica>Ei(p, z) = GAMMA(1 - p)*((z)^(p - 1)- exp(- z)*sum(((z)^(k))/(GAMMA(2 - p + k)), k = 0..infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == Gamma[1 - p]*((z)^(p - 1)- Exp[- z]*Sum[Divide[(z)^(k),Gamma[2 - p + k]], {k, 0, Infinity}, GenerateConditions->None])</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 56]
-|-
-| [https://dlmf.nist.gov/8.19.E12 8.19.E12] || [[Item:Q2698|<math>p\genexpintE{p+1}@{z}+z\genexpintE{p}@{z} = e^{-z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>p\genexpintE{p+1}@{z}+z\genexpintE{p}@{z} = e^{-z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>p*Ei(p + 1, z)+ z*Ei(p, z) = exp(- z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>p*ExpIntegralE[p + 1, z]+ z*ExpIntegralE[p, z] == Exp[- z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/8.19.E13 8.19.E13] || [[Item:Q2699|<math>\deriv{}{z}\genexpintE{p}@{z} = -\genexpintE{p-1}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}\genexpintE{p}@{z} = -\genexpintE{p-1}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(Ei(p, z), z) = - Ei(p - 1, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[ExpIntegralE[p, z], z] == - ExpIntegralE[p - 1, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/8.19.E14 8.19.E14] || [[Item:Q2700|<math>\deriv{}{z}(e^{z}\genexpintE{p}@{z}) = e^{z}\genexpintE{p}@{z}\left(1+\frac{p-1}{z}\right)-\frac{1}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{z}(e^{z}\genexpintE{p}@{z}) = e^{z}\genexpintE{p}@{z}\left(1+\frac{p-1}{z}\right)-\frac{1}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(exp(z)*Ei(p, z), z) = exp(z)*Ei(p, z)*(1 +(p - 1)/(z))-(1)/(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Exp[z]*ExpIntegralE[p, z], z] == Exp[z]*ExpIntegralE[p, z]*(1 +Divide[p - 1,z])-Divide[1,z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/8.19.E15 8.19.E15] || [[Item:Q2701|<math>\pderiv[j]{\genexpintE{p}@{z}}{p} = (-1)^{j}\int_{1}^{\infty}(\ln@@{t})^{j}t^{-p}e^{-zt}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pderiv[j]{\genexpintE{p}@{z}}{p} = (-1)^{j}\int_{1}^{\infty}(\ln@@{t})^{j}t^{-p}e^{-zt}\diff{t}</syntaxhighlight> || <math>\realpart@@{z} > 0</math> || <syntaxhighlight lang=mathematica>diff(Ei(p, z), [p$(j)]) = (- 1)^(j)* int((ln(t))^(j)* (t)^(- p)* exp(- z*t), t = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[ExpIntegralE[p, z], {p, j}] == (- 1)^(j)* Integrate[(Log[t])^(j)* (t)^(- p)* Exp[- z*t], {t, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
-|-
-| [https://dlmf.nist.gov/8.19.E16 8.19.E16] || [[Item:Q2702|<math>\genexpintE{p}@{z} = z^{p-1}e^{-z}\KummerconfhyperU@{p}{p}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = z^{p-1}e^{-z}\KummerconfhyperU@{p}{p}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(p, z) = (z)^(p - 1)* exp(- z)*KummerU(p, p, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == (z)^(p - 1)* Exp[- z]*HypergeometricU[p, p, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/8.19.E19 8.19.E19] || [[Item:Q2705|<math>\frac{n-1}{n}\genexpintE{n}@{x} < \genexpintE{n+1}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{n-1}{n}\genexpintE{n}@{x} < \genexpintE{n+1}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(n - 1)/(n)*Ei(n, x) < Ei(n + 1, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[n - 1,n]*ExpIntegralE[n, x] < ExpIntegralE[n + 1, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.19.E19 8.19.E19] || [[Item:Q2705|<math>\genexpintE{n+1}@{x} < \genexpintE{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{n+1}@{x} < \genexpintE{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(n + 1, x) < Ei(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[n + 1, x] < ExpIntegralE[n, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.19.E20 8.19.E20] || [[Item:Q2706|<math>\left(\genexpintE{n}@{x}\right)^{2} < \genexpintE{n-1}@{x}\genexpintE{n+1}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\left(\genexpintE{n}@{x}\right)^{2} < \genexpintE{n-1}@{x}\genexpintE{n+1}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(Ei(n, x))^(2) < Ei(n - 1, x)*Ei(n + 1, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(ExpIntegralE[n, x])^(2) < ExpIntegralE[n - 1, x]*ExpIntegralE[n + 1, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.19.E21 8.19.E21] || [[Item:Q2707|<math>\frac{1}{x+n} < e^{x}\genexpintE{n}@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{x+n} < e^{x}\genexpintE{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(x + n) < exp(x)*Ei(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,x + n] < Exp[x]*ExpIntegralE[n, x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.19.E21 8.19.E21] || [[Item:Q2707|<math>e^{x}\genexpintE{n}@{x} \leq \frac{1}{x+n-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>e^{x}\genexpintE{n}@{x} \leq \frac{1}{x+n-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(x)*Ei(n, x) <= (1)/(x + n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[x]*ExpIntegralE[n, x] <= Divide[1,x + n - 1]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.19.E22 8.19.E22] || [[Item:Q2708|<math>\deriv{}{x}\frac{\genexpintE{n}@{x}}{\genexpintE{n-1}@{x}} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{x}\frac{\genexpintE{n}@{x}}{\genexpintE{n-1}@{x}} > 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff((Ei(n, x))/(Ei(n - 1, x)), x) > 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[Divide[ExpIntegralE[n, x],ExpIntegralE[n - 1, x]], x] > 0</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
-|-
-| [https://dlmf.nist.gov/8.19.E23 8.19.E23] || [[Item:Q2709|<math>\int_{z}^{\infty}\genexpintE{p-1}@{t}\diff{t} = \genexpintE{p}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{z}^{\infty}\genexpintE{p-1}@{t}\diff{t} = \genexpintE{p}@{z}</syntaxhighlight> || <math>|\phase@@{z}| < \pi</math> || <syntaxhighlight lang=mathematica>int(Ei(p - 1, t), t = z..infinity) = Ei(p, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[ExpIntegralE[p - 1, t], {t, z, Infinity}, GenerateConditions->None] == ExpIntegralE[p, z]</syntaxhighlight> || Failure || Successful || Skipped - Because timed out || Successful [Tested: 70]
-|-
-| [https://dlmf.nist.gov/8.19.E24 8.19.E24] || [[Item:Q2710|<math>\int_{0}^{\infty}e^{-at}\genexpintE{n}@{t}\diff{t} = \frac{(-1)^{n-1}}{a^{n}}\left(\ln@{1+a}+\sum_{k=1}^{n-1}\frac{(-1)^{k}a^{k}}{k}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}\genexpintE{n}@{t}\diff{t} = \frac{(-1)^{n-1}}{a^{n}}\left(\ln@{1+a}+\sum_{k=1}^{n-1}\frac{(-1)^{k}a^{k}}{k}\right)</syntaxhighlight> || <math>\realpart@@{a} > -1</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*Ei(n, t), t = 0..infinity) = ((- 1)^(n - 1))/((a)^(n))*(ln(1 + a)+ sum(((- 1)^(k)* (a)^(k))/(k), k = 1..n - 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*ExpIntegralE[n, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[(- 1)^(n - 1),(a)^(n)]*(Log[1 + a]+ Sum[Divide[(- 1)^(k)* (a)^(k),k], {k, 1, n - 1}, GenerateConditions->None])</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 18]
-|-
-| [https://dlmf.nist.gov/8.19.E25 8.19.E25] || [[Item:Q2711|<math>\int_{0}^{\infty}e^{-at}t^{b-1}\genexpintE{p}@{t}\diff{t} = \frac{\EulerGamma@{b}(1+a)^{-b}}{p+b-1}\*\hyperF@{1}{b}{p+b}{a/(1+a)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-at}t^{b-1}\genexpintE{p}@{t}\diff{t} = \frac{\EulerGamma@{b}(1+a)^{-b}}{p+b-1}\*\hyperF@{1}{b}{p+b}{a/(1+a)}</syntaxhighlight> || <math>\realpart@@{a} > -1, \realpart@{p+b} > 1, \realpart@@{b} > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- a*t)*(t)^(b - 1)* Ei(p, t), t = 0..infinity) = (GAMMA(b)*(1 + a)^(- b))/(p + b - 1)* hypergeom([1, b], [p + b], a/(1 + a))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- a*t]*(t)^(b - 1)* ExpIntegralE[p, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[b]*(1 + a)^(- b),p + b - 1]* Hypergeometric2F1[1, b, p + b, a/(1 + a)]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Successful [Tested: 64]
-|-
-| [https://dlmf.nist.gov/8.19.E26 8.19.E26] || [[Item:Q2712|<math>\int_{0}^{\infty}\genexpintE{p}@{t}\genexpintE{q}@{t}\diff{t} = \frac{L(p)+L(q)}{p+q-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}\genexpintE{p}@{t}\genexpintE{q}@{t}\diff{t} = \frac{L(p)+L(q)}{p+q-1}</syntaxhighlight> || <math>p > 0, q > 0, p+q > 1</math> || <syntaxhighlight lang=mathematica>int(Ei(p, t)*Ei(q, t), t = 0..infinity) = (L(p)+ L(q))/(p + q - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[ExpIntegralE[p, t]*ExpIntegralE[q, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[L[p]+ L[q],p + q - 1]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [80 / 80]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.8698344324715543, -0.7499999999999999]
-Test Values: {Rule[L, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[p, 1.5], Rule[q, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.26794919243112303, -0.9999999999999999]
-Test Values: {Rule[L, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[p, 1.5], Rule[q, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.19.E27 8.19.E27] || [[Item:Q2713|<math>L(p) = \int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>L(p) = \int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t}</syntaxhighlight> || <math>p > 0</math> || <syntaxhighlight lang=mathematica>L(p) = int(exp(- t)*Ei(p, t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>L[p] == Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8698344324715546, 0.7499999999999999]
-Test Values: {Rule[L, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[p, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.1377836249026771, 0.24999999999999997]
-Test Values: {Rule[L, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[p, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.19.E27 8.19.E27] || [[Item:Q2713|<math>\int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t} = \frac{1}{2p}\hyperF@{1}{1}{1+p}{\tfrac{1}{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}e^{-t}\genexpintE{p}@{t}\diff{t} = \frac{1}{2p}\hyperF@{1}{1}{1+p}{\tfrac{1}{2}}</syntaxhighlight> || <math>p > 0</math> || <syntaxhighlight lang=mathematica>int(exp(- t)*Ei(p, t), t = 0..infinity) = (1)/(2*p)*hypergeom([1, 1], [1 + p], (1)/(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[Exp[- t]*ExpIntegralE[p, t], {t, 0, Infinity}, GenerateConditions->None] == Divide[1,2*p]*Hypergeometric2F1[1, 1, 1 + p, Divide[1,2]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
-|-
-| [https://dlmf.nist.gov/8.20.E1 8.20.E1] || [[Item:Q2714|<math>\genexpintE{p}@{z} = \frac{e^{-z}}{z}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{\Pochhammersym{p}{k}}{z^{k}}+(-1)^{n}\frac{\Pochhammersym{p}{n}e^{z}}{z^{n-1}}\genexpintE{n+p}@{z}\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genexpintE{p}@{z} = \frac{e^{-z}}{z}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{\Pochhammersym{p}{k}}{z^{k}}+(-1)^{n}\frac{\Pochhammersym{p}{n}e^{z}}{z^{n-1}}\genexpintE{n+p}@{z}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Ei(p, z) = (exp(- z))/(z)*(sum((- 1)^(k)*(pochhammer(p, k))/((z)^(k)), k = 0..n - 1)+(- 1)^(n)*(pochhammer(p, n)*exp(z))/((z)^(n - 1))*Ei(n + p, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>ExpIntegralE[p, z] == Divide[Exp[- z],z]*(Sum[(- 1)^(k)*Divide[Pochhammer[p, k],(z)^(k)], {k, 0, n - 1}, GenerateConditions->None]+(- 1)^(n)*Divide[Pochhammer[p, n]*Exp[z],(z)^(n - 1)]*ExpIntegralE[n + p, z])</syntaxhighlight> || Failure || Successful || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[n, 3], Rule[p, -2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
-Test Values: {Rule[n, 3], Rule[p, -2], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|-
-| [https://dlmf.nist.gov/8.20.E4 8.20.E4] || [[Item:Q2717|<math>A_{k+1}(\lambda) = (1-2k\lambda)A_{k}(\lambda)+\lambda(\lambda+1)\deriv{A_{k}(\lambda)}{\lambda}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{k+1}(\lambda) = (1-2k\lambda)A_{k}(\lambda)+\lambda(\lambda+1)\deriv{A_{k}(\lambda)}{\lambda}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[k + 1](lambda) = (1 - 2*k*lambda)*A[k](lambda)+ lambda*(lambda + 1)*diff(A[k](lambda), lambda)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, k + 1][\[Lambda]] == (1 - 2*k*\[Lambda])*Subscript[A, k][\[Lambda]]+ \[Lambda]*(\[Lambda]+ 1)*D[Subscript[A, k][\[Lambda]], \[Lambda]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.5000000000+.133974596*I
-Test Values: {lambda = 1/2*3^(1/2)+1/2*I, A[k] = 1/2*3^(1/2)+1/2*I, A[k+1] = 1/2*3^(1/2)+1/2*I, k = 1, k = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.4999999993+2.133974597*I
-Test Values: {lambda = 1/2*3^(1/2)+1/2*I, A[k] = 1/2*3^(1/2)+1/2*I, A[k+1] = 1/2*3^(1/2)+1/2*I, k = 2, k = 3}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.49999999999999944, 4.133974596215561]
-Test Values: {Rule[k, 3], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, Plus[1, k]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-1.8660254037844384, 3.7679491924311224]
-Test Values: {Rule[k, 3], Rule[λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, Plus[1, k]], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.20#Ex1 8.20#Ex1] || [[Item:Q2718|<math>A_{1}(\lambda) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{1}(\lambda) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[1](lambda) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 1][\[Lambda]] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.20#Ex2 8.20#Ex2] || [[Item:Q2719|<math>A_{2}(\lambda) = 1-2\lambda</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{2}(\lambda) = 1-2\lambda</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[2](lambda) = 1 - 2*lambda</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 2][\[Lambda]] == 1 - 2*\[Lambda]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/8.20#Ex3 8.20#Ex3] || [[Item:Q2720|<math>A_{3}(\lambda) = 1-8\lambda+6\lambda^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{3}(\lambda) = 1-8\lambda+6\lambda^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[3](lambda) = 1 - 8*lambda + 6*(lambda)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, 3][\[Lambda]] == 1 - 8*\[Lambda]+ 6*\[Lambda]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
-|-
-| [https://dlmf.nist.gov/8.21.E3 8.21.E3] || [[Item:Q2724|<math>\int_{0}^{\infty}t^{a-1}e^{+\iunit t}\diff{t} = e^{+\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}t^{a-1}e^{+\iunit t}\diff{t} = e^{+\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</syntaxhighlight> || <math>0 < \realpart@@{a}, \realpart@@{a} < 1, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(a - 1)* exp(+ I*t), t = 0..infinity) = exp(+(1)/(2)*Pi*I*a)*GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(a - 1)* Exp[+ I*t], {t, 0, Infinity}, GenerateConditions->None] == Exp[+Divide[1,2]*Pi*I*a]*Gamma[a]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/8.21.E3 8.21.E3] || [[Item:Q2724|<math>\int_{0}^{\infty}t^{a-1}e^{-\iunit t}\diff{t} = e^{-\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{\infty}t^{a-1}e^{-\iunit t}\diff{t} = e^{-\frac{1}{2}\pi\iunit a}\EulerGamma@{a}</syntaxhighlight> || <math>0 < \realpart@@{a}, \realpart@@{a} < 1, \realpart@@{a} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(a - 1)* exp(- I*t), t = 0..infinity) = exp(-(1)/(2)*Pi*I*a)*GAMMA(a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(a - 1)* Exp[- I*t], {t, 0, Infinity}, GenerateConditions->None] == Exp[-Divide[1,2]*Pi*I*a]*Gamma[a]</syntaxhighlight> || Successful || Aborted || - || Successful [Tested: 1]
-|-
-| [https://dlmf.nist.gov/8.22.E1 8.22.E1] || [[Item:Q2750|<math>\frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{\EulerGamma@{p}}{2\pi}z^{1-p}\genexpintE{p}@{z} = \frac{\EulerGamma@{p}}{2\pi}\incGamma@{1-p}{z}</syntaxhighlight> || <math>\realpart@@{p} > 0, \realpart@@{(n+p)} > 0</math> || <syntaxhighlight lang=mathematica>(GAMMA(p))/(2*Pi)*(z)^(1 - p)* Ei(p, z) = (GAMMA(p))/(2*Pi)*GAMMA(1 - p, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[Gamma[p],2*Pi]*(z)^(1 - p)* ExpIntegralE[p, z] == Divide[Gamma[p],2*Pi]*Gamma[1 - p, z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 35]
-|-
-| [https://dlmf.nist.gov/8.22.E3 8.22.E3] || [[Item:Q2752|<math>\zeta_{x}(s) = \sum_{k=1}^{\infty}k^{-s}\normincGammaP@{s}{kx}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\zeta_{x}(s) = \sum_{k=1}^{\infty}k^{-s}\normincGammaP@{s}{kx}</syntaxhighlight> || <math>\realpart@@{s} > 1</math> || <syntaxhighlight lang=mathematica>((1)/(GAMMA(s))*int(((t)^(s - 1))/(exp(t)- 1), t = 0..x)) = sum((k)^(- s)* (GAMMA(s)-GAMMA(s, k*x))/GAMMA(s), k = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(Divide[1,Gamma[s]]*Integrate[Divide[(t)^(s - 1),Exp[t]- 1], {t, 0, x}, GenerateConditions->None]) == Sum[(k)^(- s)* GammaRegularized[s, 0, k*x], {k, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Manual Skip! || Skipped - Because timed out
-|}
 </div>

Results of Incomplete Gamma and Related Functions: Difference between revisions

Latest revision as of 16:47, 25 May 2021

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