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

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=-29/8, b>=a

For fixed z and a=-29/8, b=-7/8

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

Input Form

Hypergeometric2F1[-(29/8), -(7/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (6651904 - 80628352 z + 478742817 z^2 - 1980967989 z^3 + 7999257630 z^4 + 31289970822 z^5 + 4521940829 z^6 - 341778689 z^7 + 19704468 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (6651904 - 80628352 z + 478742817 z^2 - 1980967989 z^3 + 7999257630 z^4 + 31289970822 z^5 + 4521940829 z^6 - 341778689 z^7 + 19704468 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (6651904 - 84785792 z + 528453457 z^2 - 2272234419 z^3 + 9191953680 z^4 - 98828615958 z^5 - 76138340191 z^6 - 57940519 z^7 + 3284078 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (6651904 - 80628352 z + 478742817 z^2 - 1980967989 z^3 + 7999257630 z^4 + 31289970822 z^5 + 4521940829 z^6 - 341778689 z^7 + 19704468 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/(32847007617050445 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]