Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6596)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-5/3, b>=a

For fixed z and a=-5/3, b=-4/3

http://functions.wolfram.com/07.23.03.6596.01

Input Form

Hypergeometric2F1[-(5/3), -(4/3), 9/2, z] == (1/(4775249765 z^(7/2))) (243 (-((1/Sqrt[1 - z]) (Sqrt[z] (-17280 + 178688 z - 977408 z^2 - 13852743 z^3 + 10306675 z^4 + 4362068 z^5) Cos[ArcSin[Sqrt[z]]/3])) + 3 (-17280 + 173568 z - 928256 z^2 + 5544960 z^3 + 12810447 z^4 + 2119244 z^5) Sin[ArcSin[Sqrt[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]