20.11: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/20.11.E5 20.11.E5] || [[Item:Q6846|<math>\genhyperF{2}{1}@{\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}} = \Jacobithetatau{3}^{2}@{0}{\tau}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genhyperF{2}{1}@{\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}} = \Jacobithetatau{3}^{2}@{0}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>hypergeom([(1)/(2),(1)/(2)], [1], ((JacobiTheta2(0,exp(I*Pi*tau)))^(2)/(JacobiTheta3(0,exp(I*Pi*tau)))^(2))^(2)) = (JacobiTheta3(0,exp(I*Pi*tau)))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>HypergeometricPFQ[{Divide[1,2],Divide[1,2]}, {1}, ((EllipticTheta[2, 0, Exp[I*Pi*(\[Tau])]])^(2)/(EllipticTheta[3, 0, Exp[I*Pi*(\[Tau])]])^(2))^(2)] == (EllipticTheta[3, 0, Exp[I*Pi*(\[Tau])]])^(2)</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 10]
| [https://dlmf.nist.gov/20.11.E5 20.11.E5] || <math qid="Q6846">\genhyperF{2}{1}@{\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}} = \Jacobithetatau{3}^{2}@{0}{\tau}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\genhyperF{2}{1}@{\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}} = \Jacobithetatau{3}^{2}@{0}{\tau}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>hypergeom([(1)/(2),(1)/(2)], [1], ((JacobiTheta2(0,exp(I*Pi*tau)))^(2)/(JacobiTheta3(0,exp(I*Pi*tau)))^(2))^(2)) = (JacobiTheta3(0,exp(I*Pi*tau)))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>HypergeometricPFQ[{Divide[1,2],Divide[1,2]}, {1}, ((EllipticTheta[2, 0, Exp[I*Pi*(\[Tau])]])^(2)/(EllipticTheta[3, 0, Exp[I*Pi*(\[Tau])]])^(2))^(2)] == (EllipticTheta[3, 0, Exp[I*Pi*(\[Tau])]])^(2)</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 10]
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Latest revision as of 11:56, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
20.11.E5 F 1 2 ⁡ ( 1 2 , 1 2 ; 1 ; k 2 ) = θ 3 2 ⁡ ( 0 | τ ) Gauss-hypergeometric-F-as-2F1 1 2 1 2 1 superscript 𝑘 2 Jacobi-theta-tau 3 2 0 𝜏 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\tfrac{1}{2},\tfrac{1}{2};1;k^{% 2}\right)={\theta_{3}^{2}}\left(0\middle|\tau\right)}}
\genhyperF{2}{1}@{\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}} = \Jacobithetatau{3}^{2}@{0}{\tau}		 

hypergeom([(1)/(2),(1)/(2)], [1], ((JacobiTheta2(0,exp(I*Pi*tau)))^(2)/(JacobiTheta3(0,exp(I*Pi*tau)))^(2))^(2)) = (JacobiTheta3(0,exp(I*Pi*tau)))^(2)

HypergeometricPFQ[{Divide[1,2],Divide[1,2]}, {1}, ((EllipticTheta[2, 0, Exp[I*Pi*(\[Tau])]])^(2)/(EllipticTheta[3, 0, Exp[I*Pi*(\[Tau])]])^(2))^(2)] == (EllipticTheta[3, 0, Exp[I*Pi*(\[Tau])]])^(2)
Failure Failure Error Successful [Tested: 10]
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