Generalized hypergeometric function 5F4: Specific values (formula 07.29.03.0006)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Values at z=1

For fixed a₂, a₃, a₄

http://functions.wolfram.com/07.29.03.0006.01

Input Form

HypergeometricPFQ[{1, b, c, d, b}, {b + 1, c + 1, d + 1, b + 1}, 1] == b^2 c d (((c + d - 2 b)/((b - c)^2 (b - d)^2)) PolyGamma[b] + PolyGamma[1, b]/((b - c) (b - d)) - PolyGamma[c]/((b - c)^2 (d - c)) - PolyGamma[d]/((b - d)^2 (c - d))) /; b != c && b != d && c != d

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,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]