Results 51 to 60 of about 325,732 (181)
Type-B analogue of Bell numbers using Rota's Umbral calculus approach [PDF]
International Conference on Random and Exhaustive Generation of Combinatorial StructuresRota 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
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 +3 more
doaj +1 more source
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
doaj +1 more source
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
openaire +4 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 +3 more
doaj +1 more source
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 D ′ of distributions on R d , which leads to a general theory of Sheffer polynomial sequences on D ′ .
D. Finkelshtein +3 more
semanticscholar +1 more source
Some identities of Lah–Bell polynomials
Advances in Difference Equations, 2020 Recently, the nth Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for any nonnegative integer n.
Yuankui Ma +4 more
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Bell-Based Bernoulli Polynomials with Applications
Axioms, 2021 In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind.
Ugur Duran, Serkan Araci, Mehmet Acikgoz
doaj +1 more source