8.2: Difference between revisions

Latest revision as of 11:17, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
8.2.E1	${\displaystyle{\displaystyle\gamma\left(a,z\right)=\int_{0}^{z}t^{a-1}e^{-t}% \mathrm{d}t}}$ `\incgamma@{a}{z} = \int_{0}^{z}t^{a-1}e^{-t}\diff{t}`	${\displaystyle{\displaystyle\Re a>0}}$	GAMMA(a)-GAMMA(a, z) = int((t)^(a - 1)* exp(- t), t = 0..z)	Gamma[a, 0, z] == Integrate[(t)^(a - 1)* Exp[- t], {t, 0, z}, GenerateConditions->None]	Failure	Successful	Successful [Tested: 21]	Successful [Tested: 21]
8.2.E2	${\displaystyle{\displaystyle\Gamma\left(a,z\right)=\int_{z}^{\infty}t^{a-1}e^{% -t}\mathrm{d}t}}$ `\incGamma@{a}{z} = \int_{z}^{\infty}t^{a-1}e^{-t}\diff{t}`		GAMMA(a, z) = int((t)^(a - 1)* exp(- t), t = z..infinity)	Gamma[a, z] == Integrate[(t)^(a - 1)* Exp[- t], {t, z, Infinity}, GenerateConditions->None]	Failure	Successful	Failed [14 / 42] Result: Float(infinity)+Float(infinity)I Test Values: {a = -2, z = 1/23^(1/2)+1/2I} Result: Float(infinity)+Float(infinity)I Test Values: {a = -2, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Successful [Tested: 42]
8.2.E3	${\displaystyle{\displaystyle\gamma\left(a,z\right)+\Gamma\left(a,z\right)=% \Gamma\left(a\right)}}$ `\incgamma@{a}{z}+\incGamma@{a}{z} = \EulerGamma@{a}`	${\displaystyle{\displaystyle\Re a>0}}$	GAMMA(a)-GAMMA(a, z)+ GAMMA(a, z) = GAMMA(a)	Gamma[a, 0, z]+ Gamma[a, z] == Gamma[a]	Successful	Successful	-	Successful [Tested: 7]
8.2#Ex1	${\displaystyle{\displaystyle P\left(a,z\right)=\frac{\gamma\left(a,z\right)}{% \Gamma\left(a\right)}}}$ `\normincGammaP@{a}{z} = \frac{\incgamma@{a}{z}}{\EulerGamma@{a}}`	${\displaystyle{\displaystyle\Re a>0}}$	(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = (GAMMA(a)-GAMMA(a, z))/(GAMMA(a))	GammaRegularized[a, 0, z] == Divide[Gamma[a, 0, z],Gamma[a]]	Successful	Successful	-	Successful [Tested: 21]
8.2#Ex2	${\displaystyle{\displaystyle Q\left(a,z\right)=\frac{\Gamma\left(a,z\right)}{% \Gamma\left(a\right)}}}$ `\normincGammaQ@{a}{z} = \frac{\incGamma@{a}{z}}{\EulerGamma@{a}}`	${\displaystyle{\displaystyle\Re a>0}}$	GAMMA(a, z)/GAMMA(a) = (GAMMA(a, z))/(GAMMA(a))	GammaRegularized[a, z] == Divide[Gamma[a, z],Gamma[a]]	Successful	Successful	-	Successful [Tested: 21]
8.2.E5	${\displaystyle{\displaystyle P\left(a,z\right)+Q\left(a,z\right)=1}}$ `\normincGammaP@{a}{z}+\normincGammaQ@{a}{z} = 1`	${\displaystyle{\displaystyle\Re a>0}}$	(GAMMA(a)-GAMMA(a, z))/GAMMA(a)+ GAMMA(a, z)/GAMMA(a) = 1	GammaRegularized[a, 0, z]+ GammaRegularized[a, z] == 1	Successful	Successful	-	Successful [Tested: 21]
8.2.E6	${\displaystyle{\displaystyle\gamma^{*}\left(a,z\right)=z^{-a}P\left(a,z\right)}}$ `\scincgamma@{a}{z} = z^{-a}\normincGammaP@{a}{z}`		(z)^(-(a))(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = (z)^(- a) (GAMMA(a)-GAMMA(a, z))/GAMMA(a)	Error	Successful	Missing Macro Error	Skip - symbolical successful subtest	-
8.2.E6	${\displaystyle{\displaystyle z^{-a}P\left(a,z\right)=\frac{z^{-a}}{\Gamma\left% (a\right)}\gamma\left(a,z\right)}}$ `z^{-a}\normincGammaP@{a}{z} = \frac{z^{-a}}{\EulerGamma@{a}}\incgamma@{a}{z}`	${\displaystyle{\displaystyle\Re a>0}}$	(z)^(- a)* (GAMMA(a)-GAMMA(a, z))/GAMMA(a) = ((z)^(- a))/(GAMMA(a))*GAMMA(a)-GAMMA(a, z)	(z)^(- a)* GammaRegularized[a, 0, z] == Divide[(z)^(- a),Gamma[a]]*Gamma[a, 0, z]	Failure	Successful	Failed [21 / 21] Result: .2669922311+.3869142026I Test Values: {a = 1.5, z = 1/23^(1/2)+1/2I} Result: 3.493684189-.9843316111I Test Values: {a = 1.5, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Successful [Tested: 21]
8.2.E7	${\displaystyle{\displaystyle\gamma^{*}\left(a,z\right)=\frac{1}{\Gamma\left(a% \right)}\int_{0}^{1}t^{a-1}e^{-zt}\mathrm{d}t}}$ `\scincgamma@{a}{z} = \frac{1}{\EulerGamma@{a}}\int_{0}^{1}t^{a-1}e^{-zt}\diff{t}`	${\displaystyle{\displaystyle\Re a>0}}$	(z)^(-(a))(GAMMA(a)-GAMMA(a, z))/GAMMA(a) = (1)/(GAMMA(a))int((t)^(a - 1)* exp(- z*t), t = 0..1)	Error	Failure	Missing Macro Error	Successful [Tested: 21]	-
8.2.E8	${\displaystyle{\displaystyle\gamma\left(a,ze^{2\pi mi}\right)=e^{2\pi mia}% \gamma\left(a,z\right)}}$ `\incgamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incgamma@{a}{z}`	${\displaystyle{\displaystyle\Re a>0}}$	GAMMA(a)-GAMMA(a, zexp(2PimI)) = exp(2PimIa)*GAMMA(a)-GAMMA(a, z)	Gamma[a, 0, zExp[2PimI]] == Exp[2PimIa]*Gamma[a, 0, z]	Failure	Failure	Failed [28 / 63] Result: 1.772453851+.14e-8I Test Values: {a = 1.5, z = 1/23^(1/2)+1/2I, m = 1, a = 1} Result: 1.772453851+.62e-8I Test Values: {a = 1.5, z = 1/23^(1/2)+1/2I, m = 3, a = 1} ... skip entries to safe data	Successful [Tested: 21]
8.2.E9	${\displaystyle{\displaystyle\Gamma\left(a,ze^{2\pi mi}\right)=e^{2\pi mia}% \Gamma\left(a,z\right)+(1-e^{2\pi mia})\Gamma\left(a\right)}}$ `\incGamma@{a}{ze^{2\pi mi}} = e^{2\pi mia}\incGamma@{a}{z}+(1-e^{2\pi mia})\EulerGamma@{a}`	${\displaystyle{\displaystyle\Re a>0}}$	GAMMA(a, zexp(2PimI)) = exp(2PimIa)GAMMA(a, z)+(1 - exp(2PimIa))GAMMA(a)	Gamma[a, zExp[2PimI]] == Exp[2PimIa]Gamma[a, z]+(1 - Exp[2PimIa])Gamma[a]	Failure	Failure	Failed [28 / 63] Result: -.701776495-.3980325655I Test Values: {a = 1.5, z = 1/23^(1/2)+1/2I, m = 1} Result: -.701776493-.3980325669I Test Values: {a = 1.5, z = 1/23^(1/2)+1/2I, m = 3} ... skip entries to safe data	Failed [28 / 63] 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]]]} 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]]]} ... skip entries to safe data
8.2.E10	${\displaystyle{\displaystyle e^{-\pi ia}\Gamma\left(a,ze^{\pi i}\right)-e^{\pi ia% }\Gamma\left(a,ze^{-\pi i}\right)=-\frac{2\pi i}{\Gamma\left(1-a\right)}}}$ `e^{-\pi ia}\incGamma@{a}{ze^{\pi i}}-e^{\pi ia}\incGamma@{a}{ze^{-\pi i}} = -\frac{2\pi i}{\EulerGamma@{1-a}}`	${\displaystyle{\displaystyle\Re(1-a)>0}}$	exp(- PiIa)GAMMA(a, zexp(PiI))- exp(PiIa)GAMMA(a, zexp(- PiI)) = -(2PiI)/(GAMMA(1 - a))	Exp[- PiIa]Gamma[a, zExp[PiI]]- Exp[PiIa]Gamma[a, zExp[- PiI]] == -Divide[2PiI,Gamma[1 - a]]	Failure	Failure	Failed [28 / 28] Result: -2.710645106+2.690107924I Test Values: {a = -1.5, z = 1/23^(1/2)+1/2I} Result: .1295806364+5.171352915I Test Values: {a = -1.5, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [28 / 28] Result: Complex[-2.710645107283499, 2.690107923521634] Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.12958063668571548, 5.171352913200156] Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
8.2.E11	${\displaystyle{\displaystyle\Gamma\left(a,ze^{+\pi i}\right)=\Gamma\left(a% \right)(1-z^{a}e^{+\pi ia}\gamma^{*}\left(a,-z\right))}}$ `\incGamma@{a}{ze^{+\pi i}} = \EulerGamma@{a}(1-z^{a}e^{+\pi ia}\scincgamma@{a}{-z})`	${\displaystyle{\displaystyle\Re a>0}}$	GAMMA(a, zexp(+ PiI)) = GAMMA(a)(1 - (z)^(a) exp(+ PiIa)(- z)^(-(a))(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))	Error	Failure	Missing Macro Error	Failed [4 / 21] Result: 2.046852240-1.006153525I Test Values: {a = 1.5, z = 1/23^(1/2)+1/2I} Result: -.4563214597+.8560373719I Test Values: {a = 1.5, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	-
8.2.E11	${\displaystyle{\displaystyle\Gamma\left(a,ze^{-\pi i}\right)=\Gamma\left(a% \right)(1-z^{a}e^{-\pi ia}\gamma^{*}\left(a,-z\right))}}$ `\incGamma@{a}{ze^{-\pi i}} = \EulerGamma@{a}(1-z^{a}e^{-\pi ia}\scincgamma@{a}{-z})`	${\displaystyle{\displaystyle\Re a>0}}$	GAMMA(a, zexp(- PiI)) = GAMMA(a)(1 - (z)^(a) exp(- PiIa)(- z)^(-(a))(GAMMA(a)-GAMMA(a, - z))/GAMMA(a))	Error	Failure	Missing Macro Error	Failed [10 / 21] Result: 1.510498964-.9249588863I Test Values: {a = 1.5, z = 1/2-1/2I3^(1/2)} Result: -.7017764949-.3980325647I Test Values: {a = 1.5, z = -1/23^(1/2)-1/2I} ... skip entries to safe data	-
8.2.E12	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+\left(% 1+\frac{1-a}{z}\right)\frac{\mathrm{d}w}{\mathrm{d}z}=0}}$ `\deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0`		diff(w, [z$(2)])+(1 +(1 - a)/(z))*diff(w, z) = 0	D[w, {z, 2}]+(1 +Divide[1 - a,z])*D[w, z] == 0	Successful	Successful	-	Successful [Tested: 300]
8.2.E13	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}-\left(% 1+\frac{1-a}{z}\right)\frac{\mathrm{d}w}{\mathrm{d}z}+\frac{1-a}{z^{2}}w=0}}$ `\deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0`		diff(w, [z$(2)])-(1 +(1 - a)/(z))diff(w, z)+(1 - a)/((z)^(2))w = 0	D[w, {z, 2}]-(1 +Divide[1 - a,z])D[w, z]+Divide[1 - a,(z)^(2)]w == 0	Failure	Failure	Failed [300 / 300] Result: 2.165063509-1.250000000I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = 1/23^(1/2)+1/2I} Result: -2.165063509+1.250000000I Test Values: {a = -1.5, w = 1/23^(1/2)+1/2I, z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] 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]]]} 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]]]} ... skip entries to safe data

@@ Line 14: / Line 14: @@
 ! 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.E1 8.2.E1] || <math qid="Q2480">\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
+| [https://dlmf.nist.gov/8.2.E2 8.2.E2] || <math qid="Q2481">\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.E3 8.2.E3] || <math qid="Q2482">\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#Ex1 8.2#Ex1] || <math qid="Q2483">\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#Ex2 8.2#Ex2] || <math qid="Q2484">\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.E5 8.2.E5] || <math qid="Q2485">\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] || <math qid="Q2486">\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
+| [https://dlmf.nist.gov/8.2.E6 8.2.E6] || <math qid="Q2486">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.E7 8.2.E7] || <math qid="Q2487">\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
+| [https://dlmf.nist.gov/8.2.E8 8.2.E8] || <math qid="Q2488">\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
+| [https://dlmf.nist.gov/8.2.E9 8.2.E9] || <math qid="Q2489">\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]
@@ Line 46: / Line 46: @@
 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
+| [https://dlmf.nist.gov/8.2.E10 8.2.E10] || <math qid="Q2490">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]
@@ Line 52: / Line 52: @@
 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
+| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || <math qid="Q2491">\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
+| [https://dlmf.nist.gov/8.2.E11 8.2.E11] || <math qid="Q2491">\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$(2)])+(1 +(1 - a)/(z))*diff(w, z) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]+(1 +Divide[1 - a,z])*D[w, z] == 0</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 300]
+| [https://dlmf.nist.gov/8.2.E12 8.2.E12] || <math qid="Q2492">\deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}+\left(1+\frac{1-a}{z}\right)\deriv{w}{z} = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(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$(2)])-(1 +(1 - a)/(z))*diff(w, z)+(1 - a)/((z)^(2))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {z, 2}]-(1 +Divide[1 - a,z])*D[w, z]+Divide[1 - a,(z)^(2)]*w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.165063509-1.250000000*I
+| [https://dlmf.nist.gov/8.2.E13 8.2.E13] || <math qid="Q2493">\deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{z}-\left(1+\frac{1-a}{z}\right)\deriv{w}{z}+\frac{1-a}{z^{2}}w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [z$(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]

8.2: Difference between revisions

Latest revision as of 11:17, 28 June 2021

Navigation menu

Search