Results 21 to 30 of about 144 (134)
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 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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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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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 +3 more sources
On Degenerate Poly-Daehee Polynomials Arising from Lambda-Umbral Calculus
Journal of Mathematics, 2023 In this article, we derived various identities between the degenerate poly-Daehee polynomials and some special polynomials by using λ-umbral calculus by finding the coefficients when expressing degenerate poly-Daehee polynomials as a linear combination ...
Sang Jo Yun, Jin-Woo Park
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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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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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Frontiers in Physics, 2013 In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential cornerstones ...
Thomas L Curtright, Cosmas K Zachos
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Open Mathematics, 2023 Hyperharmonic numbers were introduced by Conway and Guy (The Book of Numbers, Copernicus, New York, 1996), whereas harmonic numbers have been studied since antiquity.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Applications of Umbral Calculus Associated with p-Adic Invariant Integrals on Zp
Abstract and Applied Analysis, 2012 Recently, Dere and Simsek (2012) have studied the applications of umbral algebra to some special functions. In this paper, we investigate some properties of umbral calculus associated with p-adic invariant integrals on Zp.
Dae San Kim, Taekyun Kim
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