Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6597)

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/07.23.03.6597.01

Input Form

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

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]