Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4699)

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=2/3

http://functions.wolfram.com/07.23.03.4699.01

Input Form

Hypergeometric2F1[-(17/3), 2/3, 7/2, z] == (1/(2984660315 z^(5/2))) (81 ((1/Sqrt[1 - z]) (Sqrt[z] (-313344 + 3237888 z + 17109995 z^2 - 41265459 z^3 + 37129536 z^4 - 23586136 z^5 + 9842400 z^6 - 2421120 z^7 + 266240 z^8) Cos[ArcSin[Sqrt[z]]/3]) + (940032 - 9435136 z + 56541184 z^2 - 29066247 z^3 + 28343568 z^4 - 19489656 z^5 + 8731680 z^6 - 2288000 z^7 + 266240 z^8) 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]