Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6cj)

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=-19/8

http://functions.wolfram.com/07.23.03.b6cj.01

Input Form

Hypergeometric2F1[-(45/8), -(19/8), 3/2, -z] == (1/3927595) (4 (-4 (-295168 + 3870979 z - 7881034 z^2 + 2552954 z^3 + 129352 z^4 + 13547 z^5 + 874 z^6) Cosh[(3 ArcSinh[Sqrt[z]])/4] + (1/(Sqrt[z] Sqrt[1 + z])) ((-265031 + 8390581 z - 16344454 z^2 - 15027726 z^3 + 10463965 z^4 + 544065 z^5 + 55936 z^6 + 3496 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]