Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6327)

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=-8/3, b>=a

For fixed z and a=-8/3, b=11/3

http://functions.wolfram.com/07.23.03.6327.01

Input Form

Hypergeometric2F1[-(8/3), 11/3, -(9/2), -z] == (1/6561) ((1/(1 + z)^(11/2)) ((6561 + 22194 z + 19719 z^2 - 1848 z^3 + 2255 z^4 - 8998 z^5 - 24354 z^6 - 18304 z^7 - 4576 z^8) Cosh[ArcSinh[Sqrt[z]]/3]) - (1/(1 + z)^5) (Sqrt[z] (2187 + 5859 z + 2618 z^2 - 2090 z^3 + 2255 z^4 + 16918 z^5 + 16016 z^6 + 4576 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]