Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4yz)

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=-5/8

http://functions.wolfram.com/07.23.03.b4yz.01

Input Form

Hypergeometric2F1[-(47/8), -(5/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (1098088448 - 16192515200 z + 119101947765 z^2 - 622117975490 z^3 + 3215073656795 z^4 + 17315500682760 z^5 + 1936756753995 z^6 - 431836672170 z^7 + 87595605045 z^8 - 12310550460 z^9 + 853678800 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (1098088448 - 16192515200 z + 119101947765 z^2 - 622117975490 z^3 + 3215073656795 z^4 + 17315500682760 z^5 + 1936756753995 z^6 - 431836672170 z^7 + 87595605045 z^8 - 12310550460 z^9 + 853678800 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (1098088448 - 16192515200 z + 119101947765 z^2 - 622117975490 z^3 + 3215073656795 z^4 + 17315500682760 z^5 + 1936756753995 z^6 - 431836672170 z^7 + 87595605045 z^8 - 12310550460 z^9 + 853678800 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (1098088448 - 16878820480 z + 129109672805 z^2 - 694949107340 z^3 + 3592430974495 z^4 - 47952028566470 z^5 - 44968861701645 z^6 + 4328428350000 z^7 - 957110565255 z^8 + 188523664290 z^9 - 25560147600 z^10 + 1707357600 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (16598073689604712305 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]