Results 31 to 40 of about 159,564 (166)
A note on infinite series whose terms involve truncated degenerate exponentials
Applied Mathematics in Science and Engineering, 2023 The degenerate exponentials are degenerate versions of the ordinary exponential and the truncated degenerate exponentials are obtained from the Taylor expansions of them by truncating the first finitely many terms.
Dae San Kim, Hyekyung Kim, Taekyun Kim
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q-Functions and Distributions, Operational and Umbral Methods
Mathematics, 2021 The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials.
Giuseppe Dattoli +3 more
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Representations by degenerate Daehee polynomials
Open Mathematics, 2022 In this paper, we consider the problem of representing any polynomial in terms of the degenerate Daehee polynomials and more generally of the higher-order degenerate Daehee polynomials.
Kim Taekyun +3 more
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Representation by Degenerate Genocchi Polynomials
Journal of Mathematics, 2022 The aim of this study is to represent any polynomial in terms of the degenerate Genocchi polynomials and more generally of the higher-order degenerate Genocchi polynomials.
Taekyun Kim +3 more
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Degenerate Lah–Bell polynomials arising from degenerate Sheffer sequences
Advances in Difference Equations, 2020 Umbral calculus is one of the important methods for obtaining the symmetric identities for the degenerate version of special numbers and polynomials. Recently, Kim–Kim (J. Math. Anal. Appl.
Hye Kyung Kim
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Degenerate Bell polynomials associated with umbral calculus
Journal of Inequalities and Applications, 2020 Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials.
Taekyun Kim +4 more
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Formal Calculus and Umbral Calculus [PDF]
The Electronic Journal of Combinatorics, 2010 We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a ...
openaire +4 more sources
Operational Methods in the Study of Sobolev-Jacobi Polynomials
Mathematics, 2019 Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-called ...
Nicolas Behr +4 more
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, 2021 Recently, Kim-Kim introduced the lambda-umbral calculus, in which the lambda-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate some ...
Kim, Taekyun +3 more
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λ-q-Sheffer sequence and its applications
Demonstratio Mathematica, 2022 Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ-Sheffer sequence. The purpose of this article is to study λ-q-Sheffer sequence and the degenerate q-Sheffer sequence, which are derived from the ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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