Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4652)

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=-17/3, b>=a

For fixed z and a=-17/3, b=-4/3

http://functions.wolfram.com/07.23.03.4652.01

Input Form

Hypergeometric2F1[-(17/3), -(4/3), 7/2, -z] == (81 (Sqrt[z] (-294912 - 6258688 z + 720390685 z^2 - 459888207 z^3 - 1126151948 z^4 + 70906976 z^5 + 12382464 z^6 + 1683968 z^7 + 117760 z^8) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (884736 + 18513920 z + 375947264 z^2 - 3087909727 z^3 + 2515972028 z^4 + 65310432 z^5 + 11584640 z^6 + 1625088 z^7 + 117760 z^8) Sinh[ArcSinh[Sqrt[z]]/3]))/(68647187245 z^(5/2) Sqrt[1 + z])

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]