Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bf6c)

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=-31/8, b>=a

For fixed z and a=-31/8, b=11/8

http://functions.wolfram.com/07.23.03.bf6c.01

Input Form

Hypergeometric2F1[-(31/8), 11/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (23363584 - 175135616 z + 554385307 z^2 - 921538240 z^3 + 658562450 z^4 - 800429812 z^5 + 474062043 z^6 - 149558916 z^7 + 19996080 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (23363584 - 175135616 z + 554385307 z^2 - 921538240 z^3 + 658562450 z^4 - 800429812 z^5 + 474062043 z^6 - 149558916 z^7 + 19996080 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (23363584 - 175135616 z + 554385307 z^2 - 921538240 z^3 + 658562450 z^4 - 800429812 z^5 + 474062043 z^6 - 149558916 z^7 + 19996080 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (23363584 - 189737856 z + 661449387 z^2 - 1251193790 z^3 + 1185412410 z^4 + 2097244968 z^5 - 2087984717 z^6 + 1107739854 z^7 - 321113520 z^8 + 39992160 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (848502200010465 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]