Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4742)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-17/3, b>=a

For fixed z and a=-17/3, b=5/3

http://functions.wolfram.com/07.23.03.4742.01

Input Form

Hypergeometric2F1[-(17/3), 5/3, 3/2, z] == (1/1416545) (3 ((1/Sqrt[1 - z]) ((440267 - 2764873 z + 7125830 z^2 - 9710440 z^3 + 7405216 z^4 - 3001856 z^5 + 505856 z^6) Cos[ArcSin[Sqrt[z]]/3]) + (1/Sqrt[z]) ((95744 - 1225575 z + 4247806 z^2 - 6975448 z^3 + 6093984 z^4 - 2748928 z^5 + 505856 z^6) Sin[ArcSin[Sqrt[z]]/3])))

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]