Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2oa)

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=9/8, b>=a

For fixed z and a=9/8, b=39/8

http://functions.wolfram.com/07.23.03.c2oa.01

Input Form

Hypergeometric2F1[9/8, 39/8, -(9/2), z] == (1/(5110784 (1 - z)^(21/2))) (4 Sqrt[1 - z] (1277696 - 14374080 z + 76280305 z^2 - 261355141 z^3 + 710175807 z^4 - 2574292204 z^5 - 1122964245 z^6 + 183499095 z^7 - 27437683 z^8 + 2148146 z^9) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (1277696 - 14773360 z + 80602511 z^2 - 283382563 z^3 + 782764198 z^4 - 44835835214 z^5 - 4845673365 z^6 + 787797673 z^7 - 114047024 z^8 + 8592584 z^9) 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]