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

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=41/8, b>=a

For fixed z and a=41/8, b=47/8

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

Input Form

Hypergeometric2F1[41/8, 47/8, -(7/2), -z] == (1/(55552 (1 + z)^(29/2))) ((-Sqrt[1 + z]) (-55552 - 1257360 z - 15809225 z^2 - 170720627 z^3 - 3112925109 z^4 + 24962745625 z^5 - 36466537867 z^6 + 14551337655 z^7 - 1381470135 z^8 + 10407027 z^9) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-13888 - 318680 z - 4048693 z^2 - 43874579 z^3 - 33613865177 z^4 + 127036933937 z^5 - 122971674175 z^6 + 35296989447 z^7 - 2427501747 z^8 + 10407027 z^9) 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]