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

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=-31/8, b>=a

For fixed z and a=-31/8, b=-3/8

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

Input Form

Hypergeometric2F1[-(31/8), -(3/8), 7/2, -z] == -((1/(9625077 z^(5/2) (1 + z)^(1/8))) (64 (4 Sqrt[z] (-31 - 372 z - 41336 z^2 + 22622 z^3 + 4143 z^4 + 798 z^5 + 80 z^6) Cos[ArcTan[Sqrt[z]]/4] + (496 + 6107 z + 61628 z^2 - 187966 z^3 - 3908 z^4 - 773 z^5 - 80 z^6) Sin[ArcTan[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]