Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7ih)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-23/8

http://functions.wolfram.com/07.23.03.b7ih.01

Input Form

Hypergeometric2F1[-(43/8), -(23/8), 9/2, -z] == (256 (Sqrt[z] (400 + 9065 z + 128005 z^2 + 11406161 z^3 - 57054283 z^4 + 65921635 z^5 - 20036905 z^6 + 890035 z^7 + 25823 z^8 + 816 z^9) Cos[(5 ArcTan[Sqrt[z]])/4] - 2 (160 + 3596 z + 50527 z^2 + 1016540 z^3 - 15841475 z^4 + 36086050 z^5 - 21714823 z^6 + 2986264 z^7 + 16235 z^8 + 510 z^9) Sin[(5 ArcTan[Sqrt[z]])/4]))/(2263316913 z^(7/2) (1 + z)^(5/8))

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]