Results 41 to 50 of about 52,395 (273)
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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Normal ordering of degenerate integral powers of number operator and its applications
Applied Mathematics in Science and Engineering, 2022 The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a ‘degenerate version’ of this, we consider the normal ordering of a degenerate integral
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Two closed forms for the Bernoulli polynomials [PDF]
, 2015 In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 ...
Chapman, Robin J., Qi, Feng
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Some Identities of Degenerate Bell Polynomials
Mathematics, 2020 The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers.
Taekyun Kim +3 more
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Axioms, 2021 In this article, we derive representation formulas for a class of r-associated Stirling numbers of the second kind and examine their connections with a class of generalized Bernoulli polynomials.
P. Ricci, R. Srivastava, P. Natalini
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Asymptotics of Stirling and Chebyshev‐Stirling Numbers of the Second Kind
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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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 Bernoulli numbers and polynomials arising from Gauss hypergeometric function
Advances in Difference Equations, 2021 A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim +4 more
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Degenerate Catalan-Daehee numbers and polynomials of order r arising from degenerate umbral calculus
AIMS Mathematics, 2022 Many mathematicians have studied degenerate versions of some special polynomials and numbers that can take into account the surrounding environment or a person's psychological burden in recent years, and they've discovered some interesting results ...
Hye Kyung Kim, Dmitry V. Dolgy
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On the P-Adic Valuations of Stirling Numbers of the Second Kind
, 2021 In this paper, we introduced certain formulas for p-adic valuations of Stirling numbers of the second kind S(n, k) denoted by vp(S(n, k)) for an odd prime p and positive integers k such that n ≥ k. We have obtained the formulas, vp(S(n, n − a)) for a = 1,
S. Singh +2 more
semanticscholar +1 more source