Results 31 to 40 of about 3,137 (142)

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, Mohd Ghayasuddin, Dojin Kim, Junesang Choi   +3 more
doaj   +1 more source

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

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

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, Dae San Kim, Lee-Chae Jang, Hyunseok Lee   +3 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

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

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
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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, Dae San Kim, Taekyun Kim, Hanyoung Kim, Hyunseok Lee   +4 more
doaj   +1 more source

Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family

Fractal and Fractional, 2022
The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques.
Tabinda Nahid, Junesang Choi
doaj   +1 more source

Non-archimedean umbral calculus [PDF]

Annales mathématiques Blaise Pascal, 1998
The famous \textit{K. Mahler's} theorem [J. Reine Angew. Math. 199, 23-34 (1958; Zbl 0080.03504)] states that every continuous function \(f: Z_p\to Q_p\) can be written as \(f(x)= \sum^\infty_{n= 0}a_n\left(\begin{smallmatrix} x\\ n\end{smallmatrix}\right)\), i.e. the functions \(\left(\begin{smallmatrix} x\\ n\end{smallmatrix}\right)\) form a basis of
openaire   +1 more source