Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7lo)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-9/8

http://functions.wolfram.com/07.23.03.b7lo.01

Input Form

Hypergeometric2F1[-(43/8), -(9/8), 3, z] == (1/(724046417325 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-16 (1132362 - 26044326 z - 2107370939 z^2 - 3414554022 z^3 - 35577600 z^4 + 7386330 z^5 - 1201815 z^6 + 99450 z^7) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-566181 - 1872926748 z - 3592112726 z^2 - 134424780 z^3 + 28189995 z^4 - 4687920 z^5 + 397800 z^6) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 8 (1132362 - 26044326 z - 2107370939 z^2 - 3414554022 z^3 - 35577600 z^4 + 7386330 z^5 - 1201815 z^6 + 99450 z^7) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-566181 + 1144251801 z + 2717408338 z^2 + 657030450 z^3 - 69106785 z^4 + 13817685 z^5 - 2089980 z^6 + 159120 z^7) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

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]