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

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=-37/8, b>=a

For fixed z and a=-37/8, b=1/8

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

Input Form

Hypergeometric2F1[-(37/8), 1/8, 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (1785472 - 18594017 z + 111592000 z^2 + 309232010 z^3 - 124286020 z^4 + 46615871 z^5 - 11327316 z^6 + 1275120 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (1785472 - 18594017 z + 111592000 z^2 + 309232010 z^3 - 124286020 z^4 + 46615871 z^5 - 11327316 z^6 + 1275120 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (1785472 - 19709937 z + 123030180 z^2 - 1354046750 z^3 - 22796220 z^4 + 8303391 z^5 - 1951136 z^6 + 212520 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (1785472 - 18594017 z + 111592000 z^2 + 309232010 z^3 - 124286020 z^4 + 46615871 z^5 - 11327316 z^6 + 1275120 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (1633643063325 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)

Standard Form

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MathML Form

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<times /> <cn type='integer'> 1275120 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11327316 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 46615871 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 124286020 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 309232010 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 111592000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18594017 </cn> <ci> z </ci> 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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]