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

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=-39/8, b>=a

For fixed z and a=-39/8, b=31/8

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

Input Form

Hypergeometric2F1[-(39/8), 31/8, 5/2, -z] == (1/(4375035 z^(3/2))) (16 (Sqrt[z] (-403 + 285706 z + 2294165 z^2 + 6545576 z^3 + 8706864 z^4 + 5526720 z^5 + 1357056 z^6) Cosh[ArcSinh[Sqrt[z]]/4] - (1/Sqrt[1 + z]) ((-1612 + 47957 z + 979990 z^2 + 4771005 z^3 + 10292984 z^4 + 11300592 z^5 + 6205248 z^6 + 1357056 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]