Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b56l)

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=-47/8, b>=a

For fixed z and a=-47/8, b=11/8

http://functions.wolfram.com/07.23.03.b56l.01

Input Form

Hypergeometric2F1[-(47/8), 11/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[1 - z] (-34315264 + 277739168 z - 921183879 z^2 + 1280790420 z^3 - 3056595290 z^4 + 3638965932 z^5 - 2678892839 z^6 + 1226778072 z^7 - 321899760 z^8 + 37128000 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-34315264 + 277739168 z - 921183879 z^2 + 1280790420 z^3 - 3056595290 z^4 + 3638965932 z^5 - 2678892839 z^6 + 1226778072 z^7 - 321899760 z^8 + 37128000 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-34315264 + 277739168 z - 921183879 z^2 + 1280790420 z^3 - 3056595290 z^4 + 3638965932 z^5 - 2678892839 z^6 + 1226778072 z^7 - 321899760 z^8 + 37128000 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 4 (-8578816 + 74796552 z - 272813051 z^2 + 457425150 z^3 + 1317135610 z^4 - 2394999712 z^5 + 2489639509 z^6 - 1658161102 z^7 + 699637380 z^8 - 171160080 z^9 + 18564000 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (296338080463425 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]