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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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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.
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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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A Note on Some Identities of New Type Degenerate Bell Polynomials
Mathematics, 2019 Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced.
Taekyun Kim +3 more
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Maximum Stirling Numbers of the Second Kind
, 2008 See the abstract in the attached ...
G. KEMKES +2 more
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Generalized q-Stirling Numbers and Their Interpolation Functions
Axioms, 2013 In this paper, we define the generating functions for the generalized q-Stirling numbers of the second kind. By applying Mellin transform to these functions, we construct interpolation functions of these numbers at negative integers.
Yilmaz Simsek +2 more
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Dirichlet series and series with Stirling numbers
Cubo, 2023 This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers, derangement numbers ...
Khristo Boyadzhiev
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On the asymptotic normality of the Legendre-Stirling numbers of the second kind
, 2014 For the Legendre-Stirling numbers of the second kind asymptotic formulae are derived in terms of a local central limit theorem. Thereby, supplements of the recently published asymptotic analysis of the Chebyshev-Stirling numbers are established. Moreover,
Gawronski, Wolfgang +2 more
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Some identities related to degenerate r-Bell and degenerate Fubini polynomials
Applied Mathematics in Science and Engineering, 2023 Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the pioneering work of Carlitz on the degenerate Bernoulli and degenerate Euler polynomials.
Taekyun Kim, Dae San Kim, Jongkyum Kwon
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