Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b64s)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-43/8

http://functions.wolfram.com/07.23.03.b64s.01

Input Form

Hypergeometric2F1[-(45/8), -(43/8), 3/2, -z] == (1/817500845) (4 ((233961845 - 6193427730 z + 33385150155 z^2 - 53548406012 z^3 + 27338999739 z^4 - 3855856722 z^5 + 82135461 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + (1/(Sqrt[z] Sqrt[1 + z])) ((-39448845 + 2654983245 z - 18399536225 z^2 + 20570637521 z^3 + 17461348825 z^4 - 20502651321 z^5 + 3618470229 z^6 - 82135461 z^7) 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]