Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b64o)

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.b64o.01

Input Form

Hypergeometric2F1[-(45/8), -(43/8), -(1/2), -z] == (1/(242420 Sqrt[1 + z])) ((-Sqrt[1 + z]) (-242420 - 14727015 z + 460783065 z^2 - 1809993382 z^3 + 1715974974 z^4 - 389501667 z^5 + 12232941 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-181815 + 213293530 z - 1041462661 z^2 + 197521180 z^3 + 1083518511 z^4 - 356707734 z^5 + 12232941 z^6) 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]