Results 21 to 30 of about 160,501 (202)
Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials [PDF]
, 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 +3 more
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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
Ann Verdoodt
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(Discrete) Almansi Type Decompositions: An umbral calculus framework based on $\mathfrak{osp}(1|2)$ symmetries [PDF]
, 2011 We introduce the umbral calculus formalism for hypercomplex variables starting from the fact that the algebra of multivariate polynomials $\BR[\underline{x}]$ shall be described in terms of the generators of the Weyl-Heisenberg algebra. The extension of $
Abul-ez +39 more
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Identities involving Laguerre polynomials derived from umbral calculus [PDF]
, 2013 In this paper, we investigate some identities of Laguerre polynomials involving Bernoulli and Euler polynomials which are derived from umbral calculus.Comment: 12 ...
Kim, Taekyun
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Formal Calculus and Umbral Calculus [PDF]
The Electronic Journal of Combinatorics, 2010 We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a ...
Thomas J. Robinson
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Umbral calculus in Ore extensions
Journal of Pure and Applied Algebra, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chahrazed Benouaret, A. Salinier
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On Poly-Bernoulli polynomials of the second kind with umbral calculus viewpoint
, 2015 Poly-Bernoulli polynomials of the second kind were introduced in Kim et al. (Adv. Differ. Equ. 2014:219, 2014) as a generalization of the Bernoulli polynomial of the second kind. Here we investigate those polynomials and derive further results about them
Dae San Kim +3 more
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Identities related to the Stirling numbers and modified Apostol-type numbers on Umbral Calculus [PDF]
, 2017 By using umbral calculus and umbral algebra methods, we derive several interesting identities and relations related to the modi ed and uni cation of the Bernoulli, Euler and Genocchi polynomials and numbers and the generalized (β-) Stirling numbers of ...
T. Komatsu, Y. Simsek
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Study of Degenerate Poly-Bernoulli Polynomials by λ-Umbral Calculus
Computer Modeling in Engineering & Sciences, 2021 L. Jang +4 more
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Umbral calculus, binomial enumeration and chromatic polynomials [PDF]
Transactions of the American Mathematical Society, 1988 We develop the concept of partition categories, in order to extend the Mullin-Rota theory of binomial enumeration, and simultaneously to provide a natural setting for recent applications of the Roman-Rota umbral calculus to computations in algebraic topology. As a further application, we describe a generalisation of the chromatic polynomial of a graph.
Nigel Ray
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