Results 11 to 20 of about 65 (62)
Some identities related to degenerate Stirling numbers of the second kind
Demonstratio Mathematica, 2022 The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Normal ordering associated with λ-Stirling numbers in λ-shift algebra
Demonstratio Mathematica, 2023 It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Polynomials related to harmonic numbers and evaluation of harmonic number series II [PDF]
, 2010 In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series related ...
Veli Kurt, Ayhan Dil
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Fully degenerate Bell polynomials associated with degenerate Poisson random variables
Open Mathematics, 2021 Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al.
Kim Hye Kyung
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Some formulas for the restricted r-Lah numbers [PDF]
, 2018 The r-Lah numbers, which we denote here by `(r)(n, k), enumerate partitions of an (n+r)-element set into k+r contents-ordered blocks in which the smallest r elements belong to distinct blocks. In this paper, we consider a restricted version `(r) m (n,
Shattuck, Mark
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Sums of Powers and Special Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their ...
Boyadzhiev Khristo N.
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Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
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Fourier series of functions involving higher-order ordered Bell polynomials
Open Mathematics, 2017 In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the ...
Kim Taekyun +3 more
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The k‐Augmented Pascal Matrix and Its Properties
Journal of Mathematics, Volume 2025, Issue 1, 2025.We define the k‐augmented Pascal matrix and present both a generalization and an alternative version of this matrix. We derive some properties of the defined matrices and establish a connection with generalized Stirling numbers and second‐order Eulerian numbers. Additionally, we provide a factorization of the k‐augmented Pascal matrix, highlighting its
Gonca Kizilaslan +2 more
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A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
Demonstratio MathematicaIn this study, we introduce the λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers in the view of degenerate version, respectively.
Kim Taekyun, Kim Hye Kyung
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