Generalized hypergeometric function 6F5: Specific values (formula 07.30.03.0006)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Values at z==-1

For fixed a₁

http://functions.wolfram.com/07.30.03.0006.01

Input Form

HypergeometricPFQ[{a, a + 1/3, a + 2/3, 3 a - 1/3, 3 a, 3 a + 1/3}, {1/3, 2/3, 2 a, 2 a + 1/3, 2 a + 2/3}, -1] == ((Sqrt[Pi] Gamma[6 a])/3) (2^(1 - 9 a)/(Gamma[(3 a + 1)/2] Gamma[(9 a)/2]) + ((4 Sqrt[Pi])/(3^(9 (a/2)) (Gamma[2/3] Gamma[3 a] Gamma[3 a + 1/3]))) Cos[((9 a - 1)/6) Pi])

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]