Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.0664)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

Values at other z

Values at z==e^{+-Pi i/3}

http://functions.wolfram.com/07.23.03.0664.01

Input Form

Hypergeometric2F1[a, 3 a, 2 a, E^(-((Pi I)/3))] == ((-4 I)^a Sqrt[Pi] Gamma[1/2 + a] (1/(Gamma[2/3] Gamma[1/3 + a]) + 1/(Gamma[1/3] Gamma[2/3 + a])))/3^((3 a + 1)/2)

Standard Form

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MathML Form

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Rule Form

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Contributed by

Bill Gosper

Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
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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]
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