Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc3z)

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=33/8

http://functions.wolfram.com/07.23.03.bc3z.01

Input Form

Hypergeometric2F1[-(37/8), 33/8, 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-99986432 - 90612704 z - 138360131 z^2 - 453649378 z^3 + 16706003885 z^4 - 49244876248 z^5 + 59488124784 z^6 - 33356119104 z^7 + 7210038528 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-99986432 - 90612704 z - 138360131 z^2 - 453649378 z^3 + 16706003885 z^4 - 49244876248 z^5 + 59488124784 z^6 - 33356119104 z^7 + 7210038528 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 (-24996608 - 7030296 z - 17868669 z^2 - 88269272 z^3 + 1074504915 z^4 - 2631100962 z^5 + 2853027916 z^6 - 1479248496 z^7 + 300418272 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-99986432 - 90612704 z - 138360131 z^2 - 453649378 z^3 + 16706003885 z^4 - 49244876248 z^5 + 59488124784 z^6 - 33356119104 z^7 + 7210038528 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/(416578981147875 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]