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

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=-29/8, b>=a

For fixed z and a=-29/8, b=-19/8

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

Input Form

Hypergeometric2F1[-(29/8), -(19/8), 9/2, -z] == -((1/(7357507605 z^(7/2) Sqrt[1 + z])) (256 (Sqrt[z] Sqrt[1 + z] (-6960 - 116029 z - 1151619 z^2 - 44015772 z^3 + 139048570 z^4 - 78495333 z^5 + 6936777 z^6 + 67022 z^7) Cosh[(3 ArcSinh[Sqrt[z]])/4] + 2 (4640 + 81316 z + 833663 z^2 + 10836952 z^3 - 41978893 z^4 - 16660772 z^5 + 31946453 z^6 - 3485144 z^7 - 33511 z^8) Sinh[(3 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]