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

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.cdom.01

Input Form

Hypergeometric2F1[41/8, 47/8, -(9/2), -z] == (1/(285696 (1 + z)^(31/2))) ((-Sqrt[1 + z]) (-285696 - 6205952 z - 70361940 z^2 - 591359131 z^3 - 4809276109 z^4 - 70652022903 z^5 + 465801702263 z^6 - 580093173425 z^7 + 201814459641 z^8 - 16977949437 z^9 + 114477297 z^10) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-71424 - 1573808 z - 18065839 z^2 - 153136280 z^3 - 1246299076 z^4 - 699093430216 z^5 + 2239433122822 z^6 - 1880887194920 z^7 + 476881850364 z^8 - 29385355848 z^9 + 114477297 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]