Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bkg2)

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=-23/8, b>=a

For fixed z and a=-23/8, b=31/8

http://functions.wolfram.com/07.23.03.bkg2.01

Input Form

Hypergeometric2F1[-(23/8), 31/8, 9/2, -z] == (1/(4125033 z^(7/2))) (256 (Sqrt[z] (-80 + 89 z - 206 z^2 + 17457 z^3 + 47608 z^4 + 43472 z^5 + 13376 z^6) Cosh[ArcSinh[Sqrt[z]]/4] - (1/Sqrt[1 + z]) ((-320 + 136 z - 553 z^2 + 4766 z^3 + 36663 z^4 + 67672 z^5 + 50160 z^6 + 13376 z^7) Sinh[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]