Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4844)

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=11/3

http://functions.wolfram.com/07.23.03.4844.01

Input Form

Hypergeometric2F1[-(17/3), 11/3, 11/2, z] == (1/(130045913725 z^(9/2))) (6561 ((1/Sqrt[1 - z]) (Sqrt[z] (154224 - 427584 z - 3264 z^2 - 163200 z^3 + 18066429 z^4 - 70530963 z^5 + 124849478 z^6 - 124372352 z^7 + 72440160 z^8 - 23174528 z^9 + 3161600 z^10) Cos[ArcSin[Sqrt[z]]/3]) + (-462672 + 1145664 z + 288320 z^2 + 689792 z^3 + 5571104 z^4 - 37667041 z^5 + 83450822 z^6 - 95854720 z^7 + 62038496 z^8 - 21593728 z^9 + 3161600 z^10) 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]