Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4p6)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-33/8

http://functions.wolfram.com/07.23.03.b4p6.01

Input Form

Hypergeometric2F1[-(47/8), -(33/8), -(11/2), -z] == (1/(86016 Sqrt[1 + z])) ((-Sqrt[1 + z]) (-86016 - 381696 z - 652512 z^2 - 519751 z^3 - 173636 z^4 - 7395 z^5 + 1530 z^6) Cosh[ArcSinh[Sqrt[z]]/4] + 2 Sqrt[z] (-10752 - 51072 z - 95046 z^2 - 84953 z^3 - 34307 z^4 - 3315 z^5 + 765 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]