Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5956)

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=-11/3, b>=a

For fixed z and a=-11/3, b=17/3

http://functions.wolfram.com/07.23.03.5956.01

Input Form

Hypergeometric2F1[-(11/3), 17/3, -(5/2), z] == (1/(1620 (-1 + z)^4)) ((1/Sqrt[1 - z]) ((1620 + 6084 z + 31584 z^2 + 414120 z^3 - 3916887 z^4 + 10350600 z^5 - 12405328 z^6 + 7097792 z^7 - 1580800 z^8) Cos[ArcSin[Sqrt[z]]/3]) - Sqrt[z] (-540 - 2408 z - 12264 z^2 + 1607775 z^3 - 6315608 z^4 + 9449232 z^5 - 6307392 z^6 + 1580800 z^7) 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]