Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2cj)

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=9/8, b>=a

For fixed z and a=9/8, b=23/8

http://functions.wolfram.com/07.23.03.c2cj.01

Input Form

Hypergeometric2F1[9/8, 23/8, -(7/2), -z] == (1/(8960 (1 + z)^(15/2))) ((-Sqrt[1 + z]) (-8960 - 71280 z - 261883 z^2 - 636535 z^3 - 1789635 z^4 + 432419 z^5 + 27898 z^6) Cosh[ArcSinh[Sqrt[z]]/4] + 2 Sqrt[z] (-1120 - 9260 z - 35371 z^2 - 88700 z^3 - 3366602 z^4 + 223184 z^5 + 13949 z^6) 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]