Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bqu4)

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=-13/8, b>=a

For fixed z and a=-13/8, b=45/8

http://functions.wolfram.com/07.23.03.bqu4.01

Input Form

Hypergeometric2F1[-(13/8), 45/8, -(1/2), -z] == (1/(4292 (1 + z)^(9/2))) (-4 Sqrt[1 + z] (-1073 + 15022 z + 204813 z^2 + 630546 z^3 + 836196 z^4 + 516528 z^5 + 122400 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-3219 + 296170 z + 1772253 z^2 + 3966912 z^3 + 4316640 z^4 + 2310912 z^5 + 489600 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]