Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5242)

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=-14/3, b>=a

For fixed z and a=-14/3, b=2/3

http://functions.wolfram.com/07.23.03.5242.01

Input Form

Hypergeometric2F1[-(14/3), 2/3, 9/2, -z] == (243 (Sqrt[z] (-138240 - 1328128 z - 6035456 z^2 + 8819695 z^3 + 22831323 z^4 + 13407492 z^5 + 5402872 z^6 + 1302880 z^7 + 141440 z^8) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (414720 + 3861504 z + 17016832 z^2 + 58462208 z^3 + 17785179 z^4 + 11150436 z^5 + 4804472 z^6 + 1232160 z^7 + 141440 z^8) Sinh[ArcSinh[Sqrt[z]]/3]))/ (7248460765 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]