7.11: Difference between revisions

Latest revision as of 12:16, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
7.11.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{1}{\sqrt{\pi}}\incgamma@{\tfrac{1}{2}}{z^{2}}} `\erf@@{z} = \frac{1}{\sqrt{\pi}}\incgamma@{\tfrac{1}{2}}{z^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	erf(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2))	Erf[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], 0, (z)^(2)]	Failure	Failure	Failed [7 / 7] Result: .756123263e-1-.1955582163I Test Values: {z = 1/23^(1/2)+1/2I} Result: -1.938247417+2.376161732I Test Values: {z = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [2 / 7] Result: Complex[-1.955452759718527, 1.7141217559576072] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[-1.8042282364091204, -0.5063298374329108] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{1}{\sqrt{\pi}}\incGamma@{\tfrac{1}{2}}{z^{2}}} `\erfc@@{z} = \frac{1}{\sqrt{\pi}}\incGamma@{\tfrac{1}{2}}{z^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	erfc(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2), (z)^(2))	Erfc[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], (z)^(2)]	Failure	Failure	Failed [2 / 7] Result: 1.955452760-1.714121756I Test Values: {z = -1/2+1/2I3^(1/2)} Result: 1.804228236+.5063298372I Test Values: {z = -1/23^(1/2)-1/2I}	Failed [2 / 7] Result: Complex[1.9554527597185267, -1.7141217559576072] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[1.8042282364091202, 0.5063298374329108] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{z}{\sqrt{\pi}}\genexpintE{\frac{1}{2}}@{z^{2}}} `\erfc@@{z} = \frac{z}{\sqrt{\pi}}\genexpintE{\frac{1}{2}}@{z^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	erfc(z) = (z)/(sqrt(Pi))*Ei((1)/(2), (z)^(2))	Erfc[z] == Divide[z,Sqrt[Pi]]*ExpIntegralE[Divide[1,2], (z)^(2)]	Failure	Failure	Failed [2 / 7] Result: 2.000000000+.1e-9I Test Values: {z = -1/2+1/2I3^(1/2)} Result: 2.000000000+.1e-9I Test Values: {z = -1/23^(1/2)-1/2I}	Failed [2 / 7] Result: Complex[2.0000000000000004, -7.771561172376096^-16] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[1.9999999999999998, -5.551115123125783^-17] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@@{z} = \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}}} `\erf@@{z} = \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	erf(z) = (2z)/(sqrt(Pi))KummerM((1)/(2), (3)/(2), - (z)^(2))	Erf[z] == Divide[2z,Sqrt[Pi]]Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)]	Successful	Successful	-	Successful [Tested: 7]
7.11.E4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{2z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperM@{1}{\tfrac{3}{2}}{z^{2}}} `\frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{2z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperM@{1}{\tfrac{3}{2}}{z^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(2z)/(sqrt(Pi))KummerM((1)/(2), (3)/(2), - (z)^(2)) = (2z)/(sqrt(Pi))exp(- (z)^(2))*KummerM(1, (3)/(2), (z)^(2))	Divide[2z,Sqrt[Pi]]Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)] == Divide[2z,Sqrt[Pi]]Exp[- (z)^(2)]*Hypergeometric1F1[1, Divide[3,2], (z)^(2)]	Successful	Successful	-	Successful [Tested: 7]
7.11.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@@{z} = \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}} `\erfc@@{z} = \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	erfc(z) = (1)/(sqrt(Pi))exp(- (z)^(2))KummerU((1)/(2), (1)/(2), (z)^(2))	Erfc[z] == Divide[1,Sqrt[Pi]]Exp[- (z)^(2)]HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)]	Failure	Failure	Failed [2 / 7] Result: 1.955452760-1.714121756I Test Values: {z = -1/2+1/2I3^(1/2)} Result: 1.804228236+.5063298372I Test Values: {z = -1/23^(1/2)-1/2I}	Failed [2 / 7] Result: Complex[1.9554527597185267, -1.7141217559576072] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[1.8042282364091202, 0.5063298374329108] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E5	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \frac{z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{1}{\tfrac{3}{2}}{z^{2}}} `\frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \frac{z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{1}{\tfrac{3}{2}}{z^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	(1)/(sqrt(Pi))exp(- (z)^(2))KummerU((1)/(2), (1)/(2), (z)^(2)) = (z)/(sqrt(Pi))exp(- (z)^(2))KummerU(1, (3)/(2), (z)^(2))	Divide[1,Sqrt[Pi]]Exp[- (z)^(2)]HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)] == Divide[z,Sqrt[Pi]]Exp[- (z)^(2)]HypergeometricU[1, Divide[3,2], (z)^(2)]	Failure	Failure	Failed [2 / 7] Result: .4454723945e-1+1.714121756I Test Values: {z = -1/2+1/2I3^(1/2)} Result: .1957717634-.5063298372I Test Values: {z = -1/23^(1/2)-1/2I}	Failed [2 / 7] Result: Complex[0.04454724028147337, 1.7141217559576065] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} Result: Complex[0.19577176359087947, -0.5063298374329108] Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}
7.11.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z}+i\Fresnelsinint@{z} = z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}}} `\Fresnelcosint@{z}+i\Fresnelsinint@{z} = z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	FresnelC(z)+ IFresnelS(z) = zKummerM((1)/(2), (3)/(2), (1)/(2)PiI*(z)^(2))	FresnelC[z]+ IFresnelS[z] == zHypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]PiI*(z)^(2)]	Failure	Successful	Successful [Tested: 7]	Successful [Tested: 7]
7.11.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}} = ze^{\pi iz^{2}/2}\KummerconfhyperM@{1}{\tfrac{3}{2}}{-\tfrac{1}{2}\pi iz^{2}}} `z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}} = ze^{\pi iz^{2}/2}\KummerconfhyperM@{1}{\tfrac{3}{2}}{-\tfrac{1}{2}\pi iz^{2}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	zKummerM((1)/(2), (3)/(2), (1)/(2)PiI(z)^(2)) = zexp(PiI(z)^(2)/2)KummerM(1, (3)/(2), -(1)/(2)PiI*(z)^(2))	zHypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]PiI(z)^(2)] == zExp[PiI(z)^(2)/2]Hypergeometric1F1[1, Divide[3,2], -Divide[1,2]PiI*(z)^(2)]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 7]
7.11.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{z} = z\genhyperF{1}{2}@{\tfrac{1}{4}}{\tfrac{5}{4},\tfrac{1}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}} `\Fresnelcosint@{z} = z\genhyperF{1}{2}@{\tfrac{1}{4}}{\tfrac{5}{4},\tfrac{1}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	FresnelC(z) = zhypergeom([(1)/(4)], [(5)/(4),(1)/(2)], -(1)/(16)(Pi)^(2)* (z)^(4))	FresnelC[z] == zHypergeometricPFQ[{Divide[1,4]}, {Divide[5,4],Divide[1,2]}, -Divide[1,16](Pi)^(2)* (z)^(4)]	Successful	Successful	-	Successful [Tested: 7]
7.11.E8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}} `\Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	FresnelS(z) = (1)/(6)Pi(z)^(3)* hypergeom([(3)/(4)], [(7)/(4),(3)/(2)], -(1)/(16)(Pi)^(2) (z)^(4))	FresnelS[z] == Divide[1,6]Pi(z)^(3)* HypergeometricPFQ[{Divide[3,4]}, {Divide[7,4],Divide[3,2]}, -Divide[1,16](Pi)^(2) (z)^(4)]	Successful	Successful	-	Successful [Tested: 7]

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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-| [https://dlmf.nist.gov/7.11.E1 7.11.E1] || [[Item:Q2403|<math>\erf@@{z} = \frac{1}{\sqrt{\pi}}\incgamma@{\tfrac{1}{2}}{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erf@@{z} = \frac{1}{\sqrt{\pi}}\incgamma@{\tfrac{1}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erf(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erf[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], 0, (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .756123263e-1-.1955582163*I
+| [https://dlmf.nist.gov/7.11.E1 7.11.E1] || <math qid="Q2403">\erf@@{z} = \frac{1}{\sqrt{\pi}}\incgamma@{\tfrac{1}{2}}{z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erf@@{z} = \frac{1}{\sqrt{\pi}}\incgamma@{\tfrac{1}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erf(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2))-GAMMA((1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erf[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], 0, (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .756123263e-1-.1955582163*I
 Test Values: {z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.938247417+2.376161732*I
 Test Values: {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 [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.955452759718527, 1.7141217559576072]
@@ Line 20: / Line 20: @@
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/7.11.E2 7.11.E2] || [[Item:Q2404|<math>\erfc@@{z} = \frac{1}{\sqrt{\pi}}\incGamma@{\tfrac{1}{2}}{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{z} = \frac{1}{\sqrt{\pi}}\incGamma@{\tfrac{1}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.955452760-1.714121756*I
+| [https://dlmf.nist.gov/7.11.E2 7.11.E2] || <math qid="Q2404">\erfc@@{z} = \frac{1}{\sqrt{\pi}}\incGamma@{\tfrac{1}{2}}{z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{z} = \frac{1}{\sqrt{\pi}}\incGamma@{\tfrac{1}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(z) = (1)/(sqrt(Pi))*GAMMA((1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[z] == Divide[1,Sqrt[Pi]]*Gamma[Divide[1,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.955452760-1.714121756*I
 Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.804228236+.5063298372*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[1.9554527597185267, -1.7141217559576072]
@@ Line 26: / Line 26: @@
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/7.11.E3 7.11.E3] || [[Item:Q2405|<math>\erfc@@{z} = \frac{z}{\sqrt{\pi}}\genexpintE{\frac{1}{2}}@{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{z} = \frac{z}{\sqrt{\pi}}\genexpintE{\frac{1}{2}}@{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(z) = (z)/(sqrt(Pi))*Ei((1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[z] == Divide[z,Sqrt[Pi]]*ExpIntegralE[Divide[1,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.000000000+.1e-9*I
+| [https://dlmf.nist.gov/7.11.E3 7.11.E3] || <math qid="Q2405">\erfc@@{z} = \frac{z}{\sqrt{\pi}}\genexpintE{\frac{1}{2}}@{z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{z} = \frac{z}{\sqrt{\pi}}\genexpintE{\frac{1}{2}}@{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(z) = (z)/(sqrt(Pi))*Ei((1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[z] == Divide[z,Sqrt[Pi]]*ExpIntegralE[Divide[1,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 2.000000000+.1e-9*I
 Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 2.000000000+.1e-9*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[2.0000000000000004, -7.771561172376096*^-16]
@@ Line 32: / Line 32: @@
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/7.11.E4 7.11.E4] || [[Item:Q2406|<math>\erf@@{z} = \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erf@@{z} = \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erf(z) = (2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erf[z] == Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/7.11.E4 7.11.E4] || <math qid="Q2406">\erf@@{z} = \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erf@@{z} = \frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erf(z) = (2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erf[z] == Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/7.11.E4 7.11.E4] || [[Item:Q2406|<math>\frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{2z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperM@{1}{\tfrac{3}{2}}{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{2z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperM@{1}{\tfrac{3}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2)) = (2*z)/(sqrt(Pi))*exp(- (z)^(2))*KummerM(1, (3)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)] == Divide[2*z,Sqrt[Pi]]*Exp[- (z)^(2)]*Hypergeometric1F1[1, Divide[3,2], (z)^(2)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/7.11.E4 7.11.E4] || <math qid="Q2406">\frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{2z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperM@{1}{\tfrac{3}{2}}{z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2z}{\sqrt{\pi}}\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{-z^{2}} = \frac{2z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperM@{1}{\tfrac{3}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(2*z)/(sqrt(Pi))*KummerM((1)/(2), (3)/(2), - (z)^(2)) = (2*z)/(sqrt(Pi))*exp(- (z)^(2))*KummerM(1, (3)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[2*z,Sqrt[Pi]]*Hypergeometric1F1[Divide[1,2], Divide[3,2], - (z)^(2)] == Divide[2*z,Sqrt[Pi]]*Exp[- (z)^(2)]*Hypergeometric1F1[1, Divide[3,2], (z)^(2)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/7.11.E5 7.11.E5] || [[Item:Q2407|<math>\erfc@@{z} = \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{z} = \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(z) = (1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[z] == Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.955452760-1.714121756*I
+| [https://dlmf.nist.gov/7.11.E5 7.11.E5] || <math qid="Q2407">\erfc@@{z} = \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@@{z} = \frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(z) = (1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[z] == Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.955452760-1.714121756*I
 Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.804228236+.5063298372*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[1.9554527597185267, -1.7141217559576072]
@@ Line 42: / Line 42: @@
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/7.11.E5 7.11.E5] || [[Item:Q2407|<math>\frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \frac{z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{1}{\tfrac{3}{2}}{z^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \frac{z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{1}{\tfrac{3}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2)) = (z)/(sqrt(Pi))*exp(- (z)^(2))*KummerU(1, (3)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)] == Divide[z,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[1, Divide[3,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4454723945e-1+1.714121756*I
+| [https://dlmf.nist.gov/7.11.E5 7.11.E5] || <math qid="Q2407">\frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \frac{z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{1}{\tfrac{3}{2}}{z^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{\tfrac{1}{2}}{\tfrac{1}{2}}{z^{2}} = \frac{z}{\sqrt{\pi}}e^{-z^{2}}\KummerconfhyperU@{1}{\tfrac{3}{2}}{z^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(sqrt(Pi))*exp(- (z)^(2))*KummerU((1)/(2), (1)/(2), (z)^(2)) = (z)/(sqrt(Pi))*exp(- (z)^(2))*KummerU(1, (3)/(2), (z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[Divide[1,2], Divide[1,2], (z)^(2)] == Divide[z,Sqrt[Pi]]*Exp[- (z)^(2)]*HypergeometricU[1, Divide[3,2], (z)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 7]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .4454723945e-1+1.714121756*I
 Test Values: {z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1957717634-.5063298372*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[0.04454724028147337, 1.7141217559576065]
@@ Line 48: / Line 48: @@
 Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br></div></div>
 |-
-| [https://dlmf.nist.gov/7.11.E6 7.11.E6] || [[Item:Q2408|<math>\Fresnelcosint@{z}+i\Fresnelsinint@{z} = z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelcosint@{z}+i\Fresnelsinint@{z} = z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelC(z)+ I*FresnelS(z) = z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelC[z]+ I*FresnelS[z] == z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
+| [https://dlmf.nist.gov/7.11.E6 7.11.E6] || <math qid="Q2408">\Fresnelcosint@{z}+i\Fresnelsinint@{z} = z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelcosint@{z}+i\Fresnelsinint@{z} = z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelC(z)+ I*FresnelS(z) = z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelC[z]+ I*FresnelS[z] == z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)]</syntaxhighlight> || Failure || Successful || Successful [Tested: 7] || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/7.11.E6 7.11.E6] || [[Item:Q2408|<math>z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}} = ze^{\pi iz^{2}/2}\KummerconfhyperM@{1}{\tfrac{3}{2}}{-\tfrac{1}{2}\pi iz^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}} = ze^{\pi iz^{2}/2}\KummerconfhyperM@{1}{\tfrac{3}{2}}{-\tfrac{1}{2}\pi iz^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2)) = z*exp(Pi*I*(z)^(2)/2)*KummerM(1, (3)/(2), -(1)/(2)*Pi*I*(z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)] == z*Exp[Pi*I*(z)^(2)/2]*Hypergeometric1F1[1, Divide[3,2], -Divide[1,2]*Pi*I*(z)^(2)]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
+| [https://dlmf.nist.gov/7.11.E6 7.11.E6] || <math qid="Q2408">z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}} = ze^{\pi iz^{2}/2}\KummerconfhyperM@{1}{\tfrac{3}{2}}{-\tfrac{1}{2}\pi iz^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z\KummerconfhyperM@{\tfrac{1}{2}}{\tfrac{3}{2}}{\tfrac{1}{2}\pi iz^{2}} = ze^{\pi iz^{2}/2}\KummerconfhyperM@{1}{\tfrac{3}{2}}{-\tfrac{1}{2}\pi iz^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z*KummerM((1)/(2), (3)/(2), (1)/(2)*Pi*I*(z)^(2)) = z*exp(Pi*I*(z)^(2)/2)*KummerM(1, (3)/(2), -(1)/(2)*Pi*I*(z)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>z*Hypergeometric1F1[Divide[1,2], Divide[3,2], Divide[1,2]*Pi*I*(z)^(2)] == z*Exp[Pi*I*(z)^(2)/2]*Hypergeometric1F1[1, Divide[3,2], -Divide[1,2]*Pi*I*(z)^(2)]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/7.11.E7 7.11.E7] || [[Item:Q2409|<math>\Fresnelcosint@{z} = z\genhyperF{1}{2}@{\tfrac{1}{4}}{\tfrac{5}{4},\tfrac{1}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelcosint@{z} = z\genhyperF{1}{2}@{\tfrac{1}{4}}{\tfrac{5}{4},\tfrac{1}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelC(z) = z*hypergeom([(1)/(4)], [(5)/(4),(1)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelC[z] == z*HypergeometricPFQ[{Divide[1,4]}, {Divide[5,4],Divide[1,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/7.11.E7 7.11.E7] || <math qid="Q2409">\Fresnelcosint@{z} = z\genhyperF{1}{2}@{\tfrac{1}{4}}{\tfrac{5}{4},\tfrac{1}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelcosint@{z} = z\genhyperF{1}{2}@{\tfrac{1}{4}}{\tfrac{5}{4},\tfrac{1}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelC(z) = z*hypergeom([(1)/(4)], [(5)/(4),(1)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelC[z] == z*HypergeometricPFQ[{Divide[1,4]}, {Divide[5,4],Divide[1,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |-
-| [https://dlmf.nist.gov/7.11.E8 7.11.E8] || [[Item:Q2410|<math>\Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelS(z) = (1)/(6)*Pi*(z)^(3)* hypergeom([(3)/(4)], [(7)/(4),(3)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelS[z] == Divide[1,6]*Pi*(z)^(3)* HypergeometricPFQ[{Divide[3,4]}, {Divide[7,4],Divide[3,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
+| [https://dlmf.nist.gov/7.11.E8 7.11.E8] || <math qid="Q2410">\Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelsinint@{z} = \tfrac{1}{6}\pi z^{3}\genhyperF{1}{2}@{\tfrac{3}{4}}{\tfrac{7}{4},\tfrac{3}{2}}{-\tfrac{1}{16}\pi^{2}z^{4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelS(z) = (1)/(6)*Pi*(z)^(3)* hypergeom([(3)/(4)], [(7)/(4),(3)/(2)], -(1)/(16)*(Pi)^(2)* (z)^(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelS[z] == Divide[1,6]*Pi*(z)^(3)* HypergeometricPFQ[{Divide[3,4]}, {Divide[7,4],Divide[3,2]}, -Divide[1,16]*(Pi)^(2)* (z)^(4)]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7]
 |}
 </div>

7.11: Difference between revisions

Latest revision as of 12:16, 28 June 2021

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