Theta Functions - 20.11 Generalizations and Analogs

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
20.11.E5	${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\tfrac{1}{2},\tfrac{1}{2};1;k^{2}\right)={\theta_{3}^{2}}\left(0\middle|\tau\right)}}$ \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]