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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).
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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References in periodicals archive
The Stirling numbers of the first kind s(n, k) define that
A research on a certain family of numbers and polynomials related to Stirling numbers, central factorial numbers, and Euler numbers
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.
Indecomposable permutations with a given number of cycles
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])
An identity involving Norlund numbers and Stirling numbers of the first kind
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