Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5mv)

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=37/8

http://functions.wolfram.com/07.23.03.b5mv.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1098088448 + 759225216 z + 1286721867 z^2 + 3206500035 z^3 + 15492637965 z^4 - 225980414751 z^5 + 656395551812 z^6 - 901956059136 z^7 + 669389276160 z^8 - 260484956160 z^9 + 41912893440 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1098088448 + 759225216 z + 1286721867 z^2 + 3206500035 z^3 + 15492637965 z^4 - 225980414751 z^5 + 656395551812 z^6 - 901956059136 z^7 + 669389276160 z^8 - 260484956160 z^9 + 41912893440 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-1098088448 + 759225216 z + 1286721867 z^2 + 3206500035 z^3 + 15492637965 z^4 - 225980414751 z^5 + 656395551812 z^6 - 901956059136 z^7 + 669389276160 z^8 - 260484956160 z^9 + 41912893440 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-1098088448 + 1171008384 z + 1114609371 z^2 + 2705946228 z^3 + 14156051730 z^4 + 338232395844 z^5 - 1888463071957 z^6 + 4118794911792 z^7 - 4788831446784 z^8 + 3158992404480 z^9 - 1122272870400 z^10 + 167651573760 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (149532195401844255 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]