Results 41 to 50 of about 159,564 (166)
The Electronic Journal of Combinatorics, 2002 We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state ...
A. Di Bucchianico, D. Loeb
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Operator Ordering and Solution of Pseudo-Evolutionary Equations
Axioms, 2019 The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary differential ...
Nicolas Behr +2 more
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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
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Umbral calculus and Euler polynomials
Ars Comb., 2012 In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related to special polynomials (see[6]).
Dae San Kim +3 more
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Effect of Delta Operator on Umbral Composition in Finite Operator calculus [PDF]
, 2016 The main objective of this paper is to propose the matrix representation of umbral composition and investigate the effect of delta operator on umbral composition by using the sequential representation of delta operator in finite operator ...
Elango, C, Maheswaran, A
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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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More on the umbral calculus, with emphasis on the q-umbral calculus
Journal of Mathematical Analysis and Applications, 1985 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Representations of degenerate poly-Bernoulli polynomials
Journal of Inequalities and Applications, 2021 As is well known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate versions of such functions and polynomials, degenerate polylogarithm functions were introduced and degenerate poly-Bernoulli polynomials
Taekyun Kim +3 more
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Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers
Advances in Difference Equations, 2020 The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers of the first and second kinds.
Taekyun Kim +3 more
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Journal of Mathematics, 2022 Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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