Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5is)

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=-47/8, b>=a

For fixed z and a=-47/8, b=31/8

http://functions.wolfram.com/07.23.03.b5is.01

Input Form

Hypergeometric2F1[-(47/8), 31/8, 3/2, -z] == (1/690795) (4 (2 (88717 + 1414742 z + 7052041 z^2 + 16073584 z^3 + 18704016 z^4 + 10856448 z^5 + 2499840 z^6) Cosh[ArcSinh[Sqrt[z]]/4] - (1/(Sqrt[z] Sqrt[1 + z])) ((18941 + 868292 z + 7489681 z^2 + 26663418 z^3 + 48449552 z^4 + 47639520 z^5 + 24212736 z^6 + 4999680 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]