Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9sd)

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=25/8, b>=a

For fixed z and a=25/8, b=39/8

http://functions.wolfram.com/07.23.03.c9sd.01

Input Form

Hypergeometric2F1[25/8, 39/8, -(11/2), z] == -((1/(29331456 (1 - z)^(27/2))) (Sqrt[1 - z] (-29331456 + 463470336 z - 3576958560 z^2 + 18410748131 z^3 - 74894229528 z^4 + 293708761921 z^5 - 1992464343974 z^6 - 4668960665115 z^7 - 1507458036492 z^8 - 43157940969 z^9 + 811748106 z^10) Cos[ArcSin[Sqrt[z]]/4] + 2 Sqrt[z] (-3666432 + 59079552 z - 464737182 z^2 + 2433657883 z^3 - 10025858087 z^4 + 39365229379 z^5 - 6644504452483 z^6 - 7719842159271 z^7 - 1599934615101 z^8 - 21781907511 z^9 + 405874053 z^10) Sin[ArcSin[Sqrt[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]