An explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind [PDF]
, 2014 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.
Feng Qi (祁锋)
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Beta distribution and associated Stirling numbers of the second kind [PDF]
Probability and Mathematical StatisticsThis article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution.
Jakub Gismatullin, Patrick Tardivel
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Some Identities on λ-analogues of r-Stirling Numbers of the Second Kind
European Journal of Pure and Applied Mathematics, 2022 Recently, the λ-analogues of r-Stirling numbers of the first kind were studied by Kim-Kim. The aim of this paper is to introduce the λ-analogues of r-Stirling numbers of the second kind and to investigate some properties, recurrence relations and certain
Dae San Kim, Hye Kyung Kim, Taekyun Kim
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A q, r-analogue for the Stirling numbers of the second kind of Coxeter groups of type B [PDF]
Pure Mathematics and Applications, 2022 A generalization of the Stirling numbers of the second kind of type B is given in two different directions. One generalization is via their q-analogue and the other one uses r distinguished elements.
Eli Bagno, D. Garber, T. Komatsu
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Mixed r-Stirling numbers of the second kind [PDF]
Online Journal of Analytic Combinatorics, 2016 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.
Yaqubi, Daniel +2 more
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Probabilistic Poly Degenerate r-Stirling Numbers of the Second Kind and r-Bell Polynomials
European Journal of Pure and Applied MathematicsWe introduce degenerate poly r-Stirling numbers of the second kind and poly r-Bell polynomials by using degenerate polyexponential function and investigate some properties of these number and polynomials.
Si hyeon Lee
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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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THE 2-ADIC VALUATIONS OF STIRLING NUMBERS OF THE SECOND KIND [PDF]
International Journal of Number Theory, 2012 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 ...
Hong, Shaofang +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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Some Properties of the Non-central Stirling Numbers of the Second Kind with Complex Parameters
European Journal of Pure and Applied MathematicsThis work extends the non-central Stirling numbers of the second kind to complex arguments. This extension is achieved through an integral representation employing a Hankel contour.
Erwin Arlan, Maribeth Montero
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