Results 21 to 30 of about 147,953,414 (272)
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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Fully degenerate Bernoulli numbers and polynomials
Demonstratio Mathematica, 2022 The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{
Kim Taekyun, Kim Dae San, Park Jin-Woo
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q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers [PDF]
, 2016 We introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order q-differential operator having the
Zeng, Jiang +5 more
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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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Negative $q$-Stirling numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The notion of the negative $q$-binomial was recently introduced by Fu, Reiner, Stanton and Thiem. Mirroring the negative $q$-binomial, we show the classical $q$ -Stirling numbers of the second kind can be expressed as a pair of statistics on a subset of ...
Yue Cai, Margaret Readdy
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Some properties on degenerate Fubini polynomials
Applied Mathematics in Science and Engineering, 2022 The nth Fubini number enumerates the number of ordered partitions of a set with n elements and is the number of possible ways to write the Fubini formula for a summation of integration of order n. Further, Fubini polynomials are natural extensions of the
Taekyun Kim +3 more
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Mixed r-Stirling numbers of the second kind
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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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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Stirling Numbers of the Second Kind
, 2013 Educação Superior::Ciências Exatas e da Terra::MatemáticaThe Stirling numbers of the second kind, or Stirling partition numbers, sometimes denoted {n k}, count the number of ways to partition a set of n elements into k discrete, nonempty subsets.
Dickau, Robert
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On the uniformity of the approximation for $r$-associated Stirling numbers of the second Kind [PDF]
, 2020 The $r$-associated Stirling numbers of the second kind are a natural extension of Stirling numbers of the second kind. A combinatorial interpretation of $r$-associated Stirling numbers of the second kind is the number of ways to partition $n$ elements ...
Connamacher, Harold +1 more
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