Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9m8)

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=25/8, b>=a

For fixed z and a=25/8, b=31/8

http://functions.wolfram.com/07.23.03.c9m8.01

Input Form

Hypergeometric2F1[25/8, 31/8, -(7/2), -z] == (1/(41216 (1 + z)^(21/2))) ((-Sqrt[1 + z]) (-41216 - 556048 z - 3871153 z^2 - 21050497 z^3 - 171362650 z^4 + 431309310 z^5 - 125049573 z^6 + 2217891 z^7) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-10304 - 142232 z - 1009861 z^2 - 5547393 z^3 - 1192803442 z^4 + 1406637222 z^5 - 251991897 z^6 + 2217891 z^7) Sinh[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]