Results 11 to 20 of about 147,953,414 (272)
SOME REMARKS ABOUT STIRLING NUMBERS OF THE SECOND KIND
Human Research in Rehabilitation, 2013 In this paper we give a representation of Stirling numbers of the second kind, we obtain explicit formulas for some cases of Stirling numbers of the second kind and illustrate a method for founding other such formulas.
Ramiz Vugdalić, Fatih Destović
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Asymptotics of Stirling and Chebyshev‐Stirling Numbers of the Second Kind [PDF]
Studies in Applied Mathematics, 2014 For the classical Stirling numbers of the second kind, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the Chebyshev–Stirling numbers, a special case of the Jacobi–Stirling numbers.
Gawronski, Wolfgang +2 more
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A note on stirling numbers of the second kind [PDF]
Journal of Combinatorial Theory, 1968 AbstractFor fixed n, Stirling numbers of the second kind, S(n,r) have a single maximum.
Dobson, A.J.
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Applied Mathematics in Science and EngineeringIn this paper, we introduce the probabilistic Bernoulli numbers, Cauchy numbers, and Euler numbers of order α associated with the random variable Y, utilizing the generating function approach.
Aimin Xu
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Probabilistic Stirling Numbers of the Second Kind and Applications [PDF]
Journal of Theoretical Probability, 2020 AbstractAssociated with each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention, however, is focused on applications. Indeed, such numbers describe the moments of sums of i.i.d.
Adell, J.A.
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On the maximum of Stirling numbers of the second kind [PDF]
Journal of Combinatorial Theory, Series A, 1973 AbstractA technique is illustrated for finding an estimate of the Stirling numbers of the second kind, Sn, r(1 ⩽ r ⩽ n), as n → ∞, for a certain range of values of r. It is shown how the estimation can be found to any given degree of approximation. Finally, the location of the maximum of Sn, r (1 ⩽ r ⩽ n) and the value of the maximum are computed.
Menon, V.V
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An identity for Stirling numbers of the second kind [PDF]
Kathmandu University Journal of Science, Engineering and Technology, 2018 We obtain an identity satisfied by the Stirling numbers of the second kind.Kathmandu University Journal of Science, Engineering and TechnologyVol. 13, No.
O. Salas-Torres +2 more
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On (Q, R, W)-Stirling Numbers Of The Second Kind
, 2017 In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly defined (q, r, w)Stirling numbers of the second kind.
Ugur Duran, Mehmet Acikgoz, Serkan Araci
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Vector weighted Stirling numbers and an application in graph theory
Electronic Journal of Graph Theory and Applications, 2021 We introduce \textit{vector weighted Stirling numbers}, which are a generalization of ordinary Stirling numbers and restricted Stirling numbers. Some relations between vector weighted Stirling numbers and ordinary Stirling numbers and some of their ...
Fahimeh Esmaeeli +2 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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