Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5b3)

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=19/8

http://functions.wolfram.com/07.23.03.b5b3.01

Input Form

Hypergeometric2F1[-(47/8), 19/8, 2, z] == (16 2^(1/4) (-2 Sqrt[1 - z] (9148503 - 431848462 z + 2094086567 z^2 - 4200013744 z^3 + 4234077120 z^4 - 2135602560 z^5 + 430684800 z^6) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (9148503 - 431848462 z + 2094086567 z^2 - 4200013744 z^3 + 4234077120 z^4 - 2135602560 z^5 + 430684800 z^6) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (9148503 - 431848462 z + 2094086567 z^2 - 4200013744 z^3 + 4234077120 z^4 - 2135602560 z^5 + 430684800 z^6) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (9148503 + 254289263 z - 2496150363 z^2 + 7986175101 z^3 - 12583801880 z^4 + 10711799280 z^5 - 4744958400 z^6 + 861369600 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/(5534844315 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z)

Standard Form

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MathML Form

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</annotation-xml> </semantics> </math>

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]