Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2o7)

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=39/8

http://functions.wolfram.com/07.23.03.c2o7.01

Input Form

Hypergeometric2F1[9/8, 39/8, -(11/2), -z] == (1/(224874496 (1 + z)^(23/2))) ((-Sqrt[1 + z]) (-224874496 - 2704882432 z - 15227740640 z^2 - 53942105551 z^3 - 138913877699 z^4 - 303316136438 z^5 - 927765443678 z^6 + 337418847285 z^7 + 48504536873 z^8 + 6458498592 z^9 + 455406952 z^10) Cosh[ArcSinh[Sqrt[z]]/4] + 4 Sqrt[z] (-14054656 - 173447232 z - 1002696891 z^2 - 3647433495 z^3 - 9621623419 z^4 - 21288044565 z^5 - 952695214183 z^6 + 90223066583 z^7 + 12919215075 z^8 + 1671550517 z^9 + 113851738 z^10) 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]