Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6845)

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=-5/3, b>=a

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

http://functions.wolfram.com/07.23.03.6845.01

Input Form

Hypergeometric2F1[-(5/3), 17/3, -(5/2), z] == (1/(114048 (-1 + z)^6)) ((1/Sqrt[1 - z]) ((114048 - 316800 z - 108416 z^2 - 581504 z^3 + 2770987 z^4 - 4478300 z^5 + 3631472 z^6 - 1500928 z^7 + 252928 z^8) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (38016 - 78848 z - 88704 z^2 + 1493759 z^3 - 3146372 z^4 + 2975856 z^5 - 1374464 z^6 + 252928 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]