Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6324)

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=-8/3, b>=a

For fixed z and a=-8/3, b=11/3

http://functions.wolfram.com/07.23.03.6324.01

Input Form

Hypergeometric2F1[-(8/3), 11/3, -(11/2), z] == (1/(19683 (-1 + z)^6)) ((1/Sqrt[1 - z]) ((19683 - 94041 z + 159435 z^2 - 95053 z^3 - 6171 z^4 - 6171 z^5 - 21063 z^6 + 48450 z^7 - 31824 z^8 + 7072 z^9) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (6561 - 26730 z + 34839 z^2 - 8976 z^3 - 6545 z^4 - 6562 z^5 + 35190 z^6 - 28288 z^7 + 7072 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]