Results 11 to 20 of about 166,207 (201)
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
doaj +2 more sources
On the type 2 poly-Bernoulli polynomials associated with umbral calculus
Open Mathematics, 2021 Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques.
Kim Taekyun +3 more
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Two New Generalizations of Extended Bernoulli Polynomials and Numbers, and Umbral Calculus
Journal of Mathematics, 2022 Among a remarkably large number of various extensions of polynomials and numbers, and diverse introductions of new polynomials and numbers, in this paper, we choose to introduce two new generalizations of some extended Bernoulli polynomials and numbers ...
Nabiullah Khan +3 more
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Some identities of higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus [PDF]
arXiv, 2013 In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have alternative ways.
Taekyun Kim +3 more
arxiv +3 more sources
Maple umbral calculus package [PDF]
arXiv, 1995 We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
Bottreau, A. +2 more
arxiv +5 more sources
Umbral calculus in Ore extensions [PDF]
Journal of Pure and Applied Algebra, 2020 Abstract The aim of the paper is to show the existence of some ingredients for an umbral calculus on some Ore extensions, in a manner analogous to Rota's classical umbral calculus which deals with a univariate polynomial ring on a field of characteristic zero.
Chahrazed Benouaret, A. Salinier
semanticscholar +5 more sources
Extended r-central Bell polynopmials with umbral calculus viewpoint
Advances in Difference Equations, 2019 Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were investigated.
Lee-Chae Jang +3 more
doaj +3 more sources
Poly-Bernoulli polynomials arising from umbral calculus [PDF]
arXiv, 2013 In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
Dae san Lom, Taekyun Kim
arxiv +3 more sources
An infinite dimensional umbral calculus [PDF]
Journal of Functional Analysis, 2017 The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of distributions on $\mathbb R^d$, which leads to a general theory of Sheffer polynomial sequences on $\mathcal D'$. We define a sequence of monic polynomials on $\mathcal D'$, a polynomial sequence of binomial type, and a Sheffer sequence.
D. Finkelshtein +3 more
semanticscholar +6 more sources
Journal of Mathematical Analysis and Applications, 2000 AbstractIn this paper we establish weaker characteristic conditions of the operator tc and give some new results of invariant operators, basic sequences, and expansion theorem.
Xiehua Sun
openalex +3 more sources