Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8767)

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=13/3, b>=a

For fixed z and a=13/3, b=14/3

http://functions.wolfram.com/07.23.03.8767.01

Input Form

Hypergeometric2F1[13/3, 14/3, -(3/2), -z] == (1/(884736 (1 + z)^(21/2))) ((884736 + 21266432 z + 531005440 z^2 - 6075477919 z^3 + 9798182288 z^4 - 3492685760 z^5 + 206717120 z^6) Cosh[ArcSinh[Sqrt[z]]/3] - 3 Sqrt[z] Sqrt[1 + z] (98304 + 2293760 z - 405303199 z^2 + 1157553144 z^3 - 614496160 z^4 + 51972800 z^5) 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]