Results 221 to 230 of about 2,633 (260)

The modular (r,s)-Stirling numbers of the first kind

Discrete Mathematics, Algorithms and Applications
We propose a new generalization of the [Formula: see text]-Stirling numbers of the first kind and their analogs. These numbers appear as specialization of a new class of symmetric function, and they can be seen as a natural generalizations of the [Formula: see text]-Stirling numbers of the first kind and their analogs.
Bazeniar Abdelghafour, Moussa Ahmia
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The r-Stirling numbers of the first kind in terms of the Möbius function

The Ramanujan Journal, 2020
For any \(r\) positive integer, the \(r\)-Stirling number of the first kind \(\binom{n}{k}_r\) is defined as the number of permutations of \(\{1,2,\dots,n\}\) with exactly \(k\) cycles, such that the numbers \(1,2,\dots,r\) are in distinct cycles. The Möbius function of the partition lattice is defined in the following way: if \(v\) is a partition of ...
Cristina Ballantine, Mircea Merca
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Asymptotics of the Chebyshev–Stirling numbers of the first kind

Integral Transforms and Special Functions, 2015
ABSTRACTThe asymptotic behaviour of the Chebyshev–Stirling numbers of the second kind, a special case of the Jacobi–Stirling numbers, has been established in a recent paper by Gawronski, Littlejohn and Neuschel. In this paper, we provide an asymptotic formula for the Chebyshev–Stirling numbers of the first kind.
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On the analytic extension of Stirling numbers of the first kind

Journal of Difference Equations and Applications, 2010
We present an analytic extension of the unsigned Stirling numbers of the first kind that is in a certain sense unique in its coincidence with the Stirling polynomials. We examine and compare our extension to previous extensions of (signed) Stirling numbers of the first kind given by Butzer et al. (2007, J. Difference Equ. Appl., 13) and of the unsigned
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A probabilistic approach to stirling numbers of the first kind

Communications in Statistics - Theory and Methods, 1990
Let be a sequence of independent random variables which take on one of the values 0, 1 with specified probabilities where B1=l with probability one. Then the sum takes on one of the values l,…,n with the probabilities related to Stirling numbers of the first kind. Using these random variables we show several properties of the numbers.
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$λ$-analogues of r-Stirling numbers of the first kind

2018
12
Kim, Taekyun, Kim, Dae san
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Generating functions for extended Stirling numbers of the first kind

J. Integer Seq., 2014
Summary: In this paper we extend the definition of Stirling numbers of the first kind by way of a special multiset. This results in a family of number triangles for which we show how to obtain ordinary generating functions for the rows and exponential generating functions for the columns. The latter are derived via a recursive process. We also indicate
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A probabilistic approach to expressions of Stirling numbers of the first kind

1991
The authors give a new proof, based on independent discrete random variables, for two known representations of Stirling numbers of the first kind. The proof is based on a recursive formula, and the authors utilize a sequence of independent discrete random variables.
YAMATO, Hajime, FUJISAKI, Tsunehiro
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Theory and applications of Stirling's numbers of the first kind

1983
Bibliography: p. 108-111.
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Asymptotic Development of the Stirling Numbers of the First Kind

Journal of the London Mathematical Society, 1958
Moser, L., Wyman, M.
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