Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bg7q)

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=-27/8

http://functions.wolfram.com/07.23.03.bg7q.01

Input Form

Hypergeometric2F1[-(29/8), -(27/8), 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + z] (16704 + 304152 z + 2969919 z^2 + 23713938 z^3 + 868006385 z^4 - 3041074764 z^5 + 2261405553 z^6 - 400483454 z^7 + 9952767 z^8) Cosh[(3 ArcSinh[Sqrt[z]])/4] - (22272 + 424560 z + 4305543 z^2 + 34987833 z^3 + 423139203 z^4 - 1810251507 z^5 - 241607275 z^6 + 1578231307 z^7 - 372514783 z^8 + 9952767 z^9) Sinh[(3 ArcSinh[Sqrt[z]])/4]))/ (584513104175 z^(9/2) 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]