Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5g0)

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=27/8

http://functions.wolfram.com/07.23.03.b5g0.01

Input Form

Hypergeometric2F1[-(47/8), 27/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[1 - z] (-1338295296 + 2021383520 z + 3239005705 z^2 + 10200580845 z^3 - 142111631405 z^4 + 381140380703 z^5 - 492507532440 z^6 + 348294320400 z^7 - 130343678400 z^8 + 20303712000 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-1338295296 + 2021383520 z + 3239005705 z^2 + 10200580845 z^3 - 142111631405 z^4 + 381140380703 z^5 - 492507532440 z^6 + 348294320400 z^7 - 130343678400 z^8 + 20303712000 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-1338295296 + 2021383520 z + 3239005705 z^2 + 10200580845 z^3 - 142111631405 z^4 + 381140380703 z^5 - 492507532440 z^6 + 348294320400 z^7 - 130343678400 z^8 + 20303712000 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 (-669147648 + 1428909040 z + 1056434275 z^2 + 4016628460 z^3 + 60568271210 z^4 - 307351759396 z^5 + 616134423035 z^6 - 669269381040 z^7 + 417496138800 z^8 - 141510720000 z^9 + 20303712000 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (8847808402407975 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]