Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5ky)

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=35/8

http://functions.wolfram.com/07.23.03.b5ky.01

Input Form

Hypergeometric2F1[-(47/8), 35/8, 4, z] == (2048 2^(1/4) (-2 Sqrt[1 - z] (55762304 + 370732193 z + 3391045112 z^2 - 119552686067 z^3 + 537039391210 z^4 - 1033986516080 z^5 + 1015791635040 z^6 - 503261341440 z^7 + 100164979200 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (55762304 + 370732193 z + 3391045112 z^2 - 119552686067 z^3 + 537039391210 z^4 - 1033986516080 z^5 + 1015791635040 z^6 - 503261341440 z^7 + 100164979200 z^8) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (55762304 + 370732193 z + 3391045112 z^2 - 119552686067 z^3 + 537039391210 z^4 - 1033986516080 z^5 + 1015791635040 z^6 - 503261341440 z^7 + 100164979200 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (55762304 + 335880753 z + 3153619677 z^2 + 75157952783 z^3 - 662883949545 z^4 + 2013432526140 z^5 - 3073559922160 z^6 + 2560630325760 z^7 - 1116704160000 z^8 + 200329958400 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (201595634485245 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)

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]