Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.blu2)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-21/8, b>=a

For fixed z and a=-21/8, b=29/8

http://functions.wolfram.com/07.23.03.blu2.01

Input Form

Hypergeometric2F1[-(21/8), 29/8, -(9/2), -z] == (1/(3072 (1 + z)^(11/2))) ((-Sqrt[1 + z]) (-3072 - 9728 z - 7460 z^2 + 1757 z^3 - 1570 z^4 + 3861 z^5 + 14664 z^6 + 12240 z^7 + 3264 z^8) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-2304 - 7632 z - 6449 z^2 + 1017 z^3 - 835 z^4 + 9867 z^5 + 20376 z^6 + 13872 z^7 + 3264 z^8) Sinh[(3 ArcSinh[Sqrt[z]])/4])

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]