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

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=-39/8, b>=a

For fixed z and a=-39/8, b=27/8

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

Input Form

Hypergeometric2F1[-(39/8), 27/8, 5, z] == (65536 2^(1/4) (8 Sqrt[1 - z] (7118592 - 9269000 z - 13949845 z^2 - 38929800 z^3 + 427406555 z^4 - 908259986 z^5 + 876127980 z^6 - 411855600 z^7 + 76908000 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 4 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (7118592 - 9269000 z - 13949845 z^2 - 38929800 z^3 + 427406555 z^4 - 908259986 z^5 + 876127980 z^6 - 411855600 z^7 + 76908000 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 Sqrt[1 - z] (7118592 - 9269000 z - 13949845 z^2 - 38929800 z^3 + 427406555 z^4 - 908259986 z^5 + 876127980 z^6 - 411855600 z^7 + 76908000 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (28474368 - 54872480 z - 35546615 z^2 - 118411475 z^3 - 1604273005 z^4 + 6724826591 z^5 - 10752790360 z^6 + 8745818640 z^7 - 3633240000 z^8 + 615264000 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (111997574714025 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]