Results 21 to 30 of about 1,345 (195)
Extended Bell and Stirling numbers from hypergeometric exponentiation [PDF]
, 2001 12 pages, Latex. Journal of Integer Sequences (in press)
Sixdeniers, J. -M. +2 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.
Paolo Emilio Ricci +2 more
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Journal of Mathematics, 2022 Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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A formula relating Bell polynomials and Stirling numbers of the first kind
Enumerative Combinatorics and Applications, 2021 Summary: In this paper, we prove a general convolution formula involving the Bell polynomials and the Stirling numbers of the first kind. Our proof of the formula is algebraic and establishes an equivalent identity involving the associated exponential generating function, where we make use of induction, manipulation of finite sums and several ...
Mark Shattuck
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Heterogeneous Stirling Numbers and Heterogeneous Bell Polynomials
Russian Journal of Mathematical PhysicsThis paper introduces a novel generalization of Stirling and Lah numbers, termed ``heterogeneous Stirling numbers," which smoothly interpolate between these classical combinatorial sequences. Specifically, we define heterogeneous Stirling numbers of the second and first kinds, demonstrating their convergence to standard Stirling numbers for lambda=0 ...
Dae San Kim, Kim D S
exaly +3 more sources
Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals [PDF]
Abstract and Applied Analysis, 2009 This article is a short elementary review of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of analysis. Some new properties are included, and several analysis-related applications are mentioned.
Khristo N. Boyadzhiev
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, 2020 Bell and Stirling numbers of first and second kind tell the number of ways that n objects, or n cycles in the case of Stirling numbers of first kind, can be distributed in k cells. They are usually obtained through recurrence rules. However, recurrence rules only tell how many distributions are possible, not the specific form of each distribution, so ...
Tavazza, Giuseppe
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Axioms, 2022 In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling ...
José L. Cereceda
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On the Total Positivity and Accurate Computations of r-Bell Polynomial Bases
Axioms, 2023 A new class of matrices defined in terms of r-Stirling numbers is introduced. These r-Stirling matrices are totally positive and determine the linear transformation between monomial and r-Bell polynomial bases.
Esmeralda Mainar +2 more
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New Properties on Degenerate Bell Polynomials
Complexity, 2021 The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate versions of the Bell numbers and polynomials. We derive some new identities and properties of those numbers and polynomials that are associated with the ...
Taekyun Kim +4 more
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