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 ?
Theorem 2 is that the modified degenerate q-Changhee polynomials is represented by a sum of products of the degenerate Stirling numbers of the second kind, the Stirling numbers of the first kind, and q-Changhee polynomials.
Moser and Wyman ([MW58] Equation (5.7)) 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:
Asymptotic development of the Stirling numbers of the first kind. J.
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])