Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5651)

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=-10/3

http://functions.wolfram.com/07.23.03.5651.01

Input Form

Hypergeometric2F1[-(11/3), -(10/3), 11/2, z] == (6561 (-3 Sqrt[z] (4423680 - 82411520 z + 819789824 z^2 - 6598754304 z^3 - 392156103299 z^4 - 310900300165 z^5 + 451115611944 z^6 + 241936222240 z^7 + 15861521600 z^8) Cos[ArcSin[Sqrt[z]]/3] + Sqrt[1 - z] (39813120 - 729907200 z + 7167082496 z^2 - 57358221312 z^3 + 714439557120 z^4 + 4979797344899 z^5 + 5388156890688 z^6 + 1378888235520 z^7 + 61568726720 z^8) Sin[ArcSin[Sqrt[z]]/3]))/ (9316511857401385 Sqrt[1 - z] z^(9/2))

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]