Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8804)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=13/3, b>=a

For fixed z and a=13/3, b=17/3

http://functions.wolfram.com/07.23.03.8804.01

Input Form

Hypergeometric2F1[13/3, 17/3, -(3/2), -z] == (1/(3538944 (1 + z)^(23/2))) ((3538944 + 98828288 z + 2945187840 z^2 - 41496583011 z^3 + 87218836252 z^4 - 44569278600 z^5 + 4625842080 z^6 + 7256960 z^7) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-1179648 - 32112640 z + 7567626793 z^2 - 28129464748 z^3 + 21341328920 z^4 - 3174450080 z^5 + 7256960 z^6) Sinh[ArcSinh[Sqrt[z]]/3])

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]