Generalized hypergeometric function 6F5: Specific values (formula 07.30.03.0002)

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 a₃, a₄, b₁

http://functions.wolfram.com/07.30.03.0002.01

Input Form

HypergeometricPFQ[{-(n/2), (1 - n)/3, c, d, c + 1/3, c + 2/3}, {g, (d - n)/3, (d - n + 1)/3, (d - n + 2)/3, 3 b - g + 3/2}, 1] == (Pochhammer[1 + 3 c - d, n]/Pochhammer[1 - d, n]) HypergeometricPFQ[{-n, 3 c, g - 1/2, 1 + 3 c - g}, {1 + 3 c - d, 2 g - 1, 2 + 6 c - 2 g}, 4] /; Element[n, Integers] && n > 0 && Floor[(n + 1)/3] == Floor[(n + 2)/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)

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]