Generalized hypergeometric function 5F4: Specific values (formula 07.29.03.0018)

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/07.29.03.0018.01

Input Form

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