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

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=-11/8

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

Input Form

Hypergeometric2F1[-(29/8), -(11/8), 9/2, -z] == (1/(2974311585 z^(7/2) Sqrt[1 + z])) (256 (Sqrt[z] Sqrt[1 + z] (6960 + 96193 z + 758205 z^2 + 19080414 z^3 - 39189094 z^4 + 9529245 z^5 + 297321 z^6 + 14260 z^7) Cosh[(3 ArcSinh[Sqrt[z]])/4] - (9280 + 136184 z + 1120183 z^2 + 10808735 z^3 - 22269782 z^4 - 22699306 z^5 + 9676123 z^6 + 304451 z^7 + 14260 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]