Generalized hypergeometric function 6F5: Specific values (formula 07.30.03.0010)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]

Specific values

Specialized values

For fixed a₁,a₂,b₃,z

http://functions.wolfram.com/07.30.03.0010.01

Input Form

HypergeometricPFQ[{a, b, a + 1/3, a + 2/3, b + 1/3, b + 2/3}, {1/3, 2/3, g, g + 1/3, g + 2/3}, z] == (1/3) Sum[Hypergeometric2F1[3 a, 3 b, 3 g, Exp[(2 Pi I k)/3] z^(1/3)], {k, 0, 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)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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,...,a_p},{b₁,...,b_q},z]