Stirling numbers of the first kind


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Stirling numbers of the first kind

[¦stər·liŋ ‚num·bərz əv th ŋ ′fərst ‚kind]
(mathematics)
The numbers s (n, r) giving the coefficient of x r in the falling factorial polynomial x (x - 1)(x - 2)⋯(x - n + 1).
References in periodicals archive ?
Asymptotic expansions for the Stirling numbers of the first kind.
Asymptotic development of the Stirling numbers of the first kind.
The asymptotic behavior of the Stirling numbers of the first kind.
7)) give the following formula for Stirling numbers of the first kind in the asymptotic regime where n and m tend to infinity such that m/n = [mu] is fixed:
Abstract In this paper we investigate the relation for the Bernoulli numbers of higher order and the Stirling numbers of the first kind, and establish an computational formula for the Norlund numbers.
Keywords Norlund numbers, the Bernoulli numbers of higher order, the Stirling numbers of the first kind.
Stirling numbers of the first kind s(n, k) can be defined by means of (see [1], [3], [5])
Associated Stirling numbers of the first kind d(n, k) and associated Stirling numbers of the second kind b(n; k) are defined, respectively, by (see [1], [3])