Results 11 to 20 of about 51,456 (294)
Some identities related to degenerate Stirling numbers of the second kind [PDF]
Demonstratio Mathematica, 2022 The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind [PDF]
, 2015 In the paper, the author finds an explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind.Comment: 5 ...
Feng Qi
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Asymptotic Estimates for Second Kind Generalized Stirling Numbers [PDF]
Journal of Applied Mathematics, 2013 Asymptotic formulas for the generalized Stirling numbers of the second kind with integer and real parameters are obtained and ranges of validity of the formulas are established.
Cristina B. Corcino, Roberto B. Corcino
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Mixed r-stirling numbers of the second kind [PDF]
Online Journal of Analytic Combinatorics, 2014 The Stirling number of the second kind \( S(n, k) \) counts the number of ways to partition a set of \( n \) labeled balls into \( k \) non-empty unlabeled cells. We extend this problem and give a new statement of the \( r \)-Stirling numbers of the second kind and \( r \)-Bell numbers.
Daniel Yaqubi +2 more
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On 2-Adic Orders of Stirling Numbers of the Second Kind [PDF]
, 2005 We prove that for any k = 1,... , 2n the 2-adic order of the Stirling number S(2n, k) of the second kind is exactly d(k) − 1, where d(k) denotes the number of 1’s among the binary digits of k. This confirms a conjecture of Lengyel.
Stefan De Wannemacker
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Probabilistic multi-Stirling numbers of the second kind associated with random variables
Applied Mathematics in Science and EngineeringThis paper investigates a probabilistic extension of the multi-Stirling numbers of the second kind and a ‘poly' version of the probabilistic degenerate Lah-Bell polynomials.
Xiangjing Liu +4 more
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On stirling numbers of the second kind
Journal of Combinatorial Theory, 1969 AbstractWe first find inequalities between the Stirling numbers S(n, r) for fixed n, then introduce functions L and U such that L(n, r)≤S(n, r)≤U(n, r), and finally obtain the asymptotic value n/log n for the value of r for which S(n, r) is maximal.
Rennie, B.C., Dobson, A.J.
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Generalized degenerate Stirling numbers arising from degenerate Boson normal ordering
Applied Mathematics in Science and Engineering, 2023 It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results.
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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The 2-adic valuations of Stirling numbers of the second kind [PDF]
International Journal of Number Theory, 2009 In this paper, we investigate the 2-adic valuations of the Stirling numbers S(n, k) of the second kind. We show that v2(S(4i, 5)) = v2(S(4i + 3, 5)) if and only if i ≢ 7 (mod 32). This confirms a conjecture of Amdeberhan, Manna and Moll raised in 2008. We show also that v2(S(2n+ 1, k + 1)) = s2(n) - 1 for any positive integer n, where s2(n) is the sum ...
Shaofang Hong, Jianrong Zhao, Wei Zhao
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Asymptotics of the Stirling numbers of the second kind revisited
Applicable Analysis and Discrete Mathematics, 2013 Using the Saddle point method and multiseries expansions, we obtain from the generating function of the Stirling numbers of the second kind {n / m} and Cauchy's integral formula, asymptotic results in central and non-central regions. In the central region, we revisit the celebrated Gaussian theorem with more precision. In the region m = n -
Guy Louchard
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