Generalized hypergeometric function: Specific values (formula 07.31.03.0020)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]

Specific values

Specialized values

Case _q+1F_q

http://functions.wolfram.com/07.31.03.0020.01

Input Form

HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, q + 1]}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, q - n], 2 + Subscript[a, q - n + 1], 2 + Subscript[a, q - n + 2], \[Ellipsis], 2 + Subscript[a, q]}, z] == (((-1)^q 2^n)/z) ((1/z) Sum[(Pochhammer[q, k]/k!) PolyLog[n - k, z], {k, 0, n - 1}] + Sum[(((-1)^(q - k) Pochhammer[n, k])/k!) PolyLog[q - k, z], {k, 0, q - 1}] - Binomial[n + q - 1, q]) /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, q + 1] == 1

Standard Form

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MathML 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,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]