Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9pv)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-39/8, b>=a

For fixed z and a=-39/8, b=-29/8

http://functions.wolfram.com/07.23.03.b9pv.01

Input Form

Hypergeometric2F1[-(39/8), -(29/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (382959616 - 7944916096 z + 87670112309 z^2 - 752674787319 z^3 + 7329790660465 z^4 + 133169602772485 z^5 + 233346791776655 z^6 + 100285283390955 z^7 + 9358013213835 z^8 + 19617245895 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (382959616 - 7944916096 z + 87670112309 z^2 - 752674787319 z^3 + 7329790660465 z^4 + 133169602772485 z^5 + 233346791776655 z^6 + 100285283390955 z^7 + 9358013213835 z^8 + 19617245895 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (382959616 - 7944916096 z + 87670112309 z^2 - 752674787319 z^3 + 7329790660465 z^4 + 133169602772485 z^5 + 233346791776655 z^6 + 100285283390955 z^7 + 9358013213835 z^8 + 19617245895 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (382959616 - 8184265856 z + 92596416549 z^2 - 806672350289 z^3 + 7791593466475 z^4 - 207467477977845 z^5 - 824851367348615 z^6 - 727083190561715 z^7 - 171500404875735 z^8 - 7552639669575 z^9 + 39234491790 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (88114240128886756785 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^5)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]