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

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=25/8

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

Input Form

Hypergeometric2F1[-(37/8), 25/8, 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (-457080832 + 1812254080 z - 1656513495 z^2 - 1131194155 z^3 - 1493449685 z^4 + 17664823239 z^5 - 31589062960 z^6 + 25970105920 z^7 - 10595397120 z^8 + 1744364160 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-457080832 + 1812254080 z - 1656513495 z^2 - 1131194155 z^3 - 1493449685 z^4 + 17664823239 z^5 - 31589062960 z^6 + 25970105920 z^7 - 10595397120 z^8 + 1744364160 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-457080832 + 2097929600 z - 2742303655 z^2 - 259730380 z^3 - 690336010 z^4 + 4066570844 z^5 - 6344645335 z^6 + 4815897320 z^7 - 1852425520 z^8 + 290727360 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-457080832 + 1812254080 z - 1656513495 z^2 - 1131194155 z^3 - 1493449685 z^4 + 17664823239 z^5 - 31589062960 z^6 + 25970105920 z^7 - 10595397120 z^8 + 1744364160 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (3849189785806365 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]