Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b85k)

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=33/8

http://functions.wolfram.com/07.23.03.b85k.01

Input Form

Hypergeometric2F1[-(43/8), 33/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-883458048 + 1715150976 z + 862671117 z^2 + 1025731245 z^3 + 2899790355 z^4 - 113300995537 z^5 + 352480390084 z^6 - 490420485632 z^7 + 362925122560 z^8 - 140059279360 z^9 + 22304522240 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-883458048 + 2046447744 z + 310078461 z^2 + 574484988 z^3 + 2364749310 z^4 - 37780942852 z^5 + 104765468461 z^6 - 136810869536 z^7 + 96799935232 z^8 - 36060344320 z^9 + 5576130560 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-883458048 + 1715150976 z + 862671117 z^2 + 1025731245 z^3 + 2899790355 z^4 - 113300995537 z^5 + 352480390084 z^6 - 490420485632 z^7 + 362925122560 z^8 - 140059279360 z^9 + 22304522240 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-883458048 + 1715150976 z + 862671117 z^2 + 1025731245 z^3 + 2899790355 z^4 - 113300995537 z^5 + 352480390084 z^6 - 490420485632 z^7 + 362925122560 z^8 - 140059279360 z^9 + 22304522240 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(20132110633721625 Pi (1 + Sqrt[1 - z])^(1/4) 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]