Results 1 to 10 of about 325,732 (181)
Integration in the umbral calculus [PDF]
Journal of Mathematical Analysis and Applications, 1980 AbstractThe adjointness between “multiplication” and “derivation” is a recurrent theme in Rota's umbral calculus. The subject of this paper is the companion adjointness between “division” and “integration.”
Yang, Kung-Wei
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Can Umbral and q-calculus be merged? [PDF]
, 2019 The $q$-calculus is reformulated in terms of the umbral calculus and of the associated operational formalism. We show that new and interesting elements emerge from such a restyling. The proposed technique is applied to a different formulations of $q$ special functions, to the derivation of integrals involving ordinary and $q$-functions and to the study
G. Dattoli +3 more
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Umbral Methods, Function Factorisation and Mittag–Leffler Fourier-Type Integral Transform
AxiomsWe propose a systematic way to construct trigonometric-like functions beyond the classical sine–cosine pair by factorising rational expressions in the umbral operator and then evaluating their action on the vacuum.
Giuseppe Dattoli +2 more
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Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials
, 2018 This article aims to identify the generating function of modified Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modified Apostol type q-Bernoulli polynomials are given.
M. Acikgoz, R. Ates, U. Duran, S. Araci
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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
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Identities arising from higher-order Daehee polynomial bases
Open Mathematics, 2015 Here we will derive formulas for expressing any polynomial as linear combinations of two kinds of higherorder Daehee polynomial basis. Then we will apply these formulas to certain polynomials in order to get new and interesting identities involving ...
Kim Dae San, Kim Taekyun
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Degenerate ordered Bell numbers and polynomials associated with umbral calculus
, 2017 In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz’s degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell polynomials ...
Taekyun Kim +3 more
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Journal of Mathematical Analysis and Applications, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Umbral Interpolation: A Survey
MathematicsA survey on recent umbral polynomial interpolation is presented. Some new results are given, following a matrix-determinant approach. Some theoretical and numerical examples are provided.
Francesco Aldo Costabile +2 more
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, 2017 In this paper, we study partially degenerate Bell numbers and polynomials by using umbral calculus. We give some new identities for these numbers and polynomials which are associated with special numbers and polynomial. c ©2017 All rights reserved.
Taekyun Kim, D. Kim, H. Kwon, S. Rim
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