Generalized hypergeometric function: Operations (formula 07.31.25.0003)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Operations

Limit operation

http://functions.wolfram.com/07.31.25.0003.01

Input Form

Limit[(1/Gamma[Subscript[b, 1]]) HypergeometricPFQ[ {Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z], Subscript[b, 1] -> -n] == z^(n + 1) Product[Pochhammer[Subscript[a, j], n + 1] HypergeometricPFQRegularized[{Subscript[a, 1] + n + 1, \[Ellipsis], Subscript[a, p] + n + 1}, {n + 2, Subscript[b, 2] + n + 1, \[Ellipsis], Subscript[b, q] + n + 1}, z], {j, 1, p}] /; Element[n, Integers] && n >= 0

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]