Generalized hypergeometric function: Specific values (formula 07.31.03.0054)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

Specialized values

Case _q+1F_qat z==1

http://functions.wolfram.com/07.31.03.0054.01

Input Form

HypergeometricPFQ[{1, Subscript[a, 2], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[a, 2] + 1, \[Ellipsis], Subscript[a, n + 1] + 1, Subscript[a, n + 2] + 2, \[Ellipsis], Subscript[a, q + 1] + 2}, 1] == (-1)^q 2^(q - n) (Sum[Binomial[q + k - 1, k] Zeta[q - n - k], {k, 0, q - n - 2}] + Sum[(-1)^(q - k) Binomial[q - n + k - 1, k] Zeta[q - k], {k, 0, q - 2}] - Binomial[2 q - n - 1, q - n - 1]) /; Subscript[a, 2] == Subscript[a, 3] == \[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]