Results 41 to 50 of about 160,501 (202)

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
doaj   +1 more source

Type-B analogue of Bell numbers using Rota's Umbral calculus approach [PDF]

International Conference on Random and Exhaustive Generation of Combinatorial Structures
Rota used the functional L to recover old properties and obtain some new formulas for the Bell numbers. Tanny used Rota's functional L and the celebrated Worpitzky identity to obtain some expression for the ordered Bell numbers, which can be seen as an ...
Eli Bagno, David Garber
semanticscholar   +1 more source

Sheffer sequences of polynomials and their applications [PDF]

, 2013
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus.
Dolgy, Dmitry V., Kim, Dae San, Kim, Taekyun, Rim, Seog-Hoon   +3 more
core   +2 more sources

Dual Numbers and Operational Umbral Methods

Axioms, 2019
Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view,
Nicolas Behr, Giuseppe Dattoli, Ambra Lattanzi, Silvia Licciardi   +3 more
doaj   +1 more source

Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering [PDF]

, 2005
We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1 in terms of ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link between the monomiality principle and the umbral calculus.
Blasiak, P, Dattoli, G, Horzela, A, Penson, K A   +3 more
core   +2 more sources

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, Giuseppe Dattoli, Ambra Lattanzi   +2 more
doaj   +1 more source

Umbral Calculus and the Frobenius-Euler Polynomials

Abstract and Applied Analysis, 2013
We study some properties of umbral calculus related to the Appell sequence. From those properties, we derive new and interesting identities of the Frobenius-Euler polynomials.
Dae San Kim, Taekyun Kim, Sang-Hun Lee
doaj   +1 more source

Computer algebra and Umbral Calculus

Discrete Mathematics, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bottreau, A., Di Bucchianico, A., Loeb, D.E.   +2 more
openaire   +2 more sources

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, Dae San Kim, Jongkyum Kwon, Hyunseok Lee   +3 more
doaj   +1 more source

Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

, 1995
`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a ...
A Dimakis, Arshansky R I, Dorfmeister G, Dunford N, F Müller-Hoissen, Macrea K I, Milne-Thomson L M, Montvay I, Putnam C R, Reed M, Riordan J, Roman S, Roman S, Rota G-C, Rota G-C, Schild A, Schmüdgen K, Smirnov Y, T Striker, Turbiner A, Turbiner A, Turbiner A, Turbiner A, Yamamoto H, Zakhar'ev B N   +24 more
core   +2 more sources