Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8037)

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=4/3, b>=a

For fixed z and a=4/3, b=17/3

http://functions.wolfram.com/07.23.03.8037.01

Input Form

Hypergeometric2F1[4/3, 17/3, -(5/2), -z] == (1/(829440 (1 + z)^(19/2))) ((829440 + 10432512 z + 70862848 z^2 + 533585920 z^3 - 1341094099 z^4 - 64984200 z^5 - 15880856 z^6 - 2840224 z^7 - 250240 z^8) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (276480 + 3282944 z + 21331968 z^2 - 522975865 z^3 + 58030656 z^4 + 14554584 z^5 + 2715104 z^6 + 250240 z^7) Sinh[ArcSinh[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]