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Maple umbral calculus package [PDF]
, 1995 We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
Anne Bottreau +2 more
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Applications of Umbral Calculus Associated with p-Adic Invariant Integrals on Zp [PDF]
Abstract and Applied Analysis, 2012 Recently, Dere and Simsek (2012) have studied the applications of umbral algebra to some special functions. In this paper, we investigate some properties of umbral calculus associated with p-adic invariant integrals on Zp.
Dae San Kim, Taekyun Kim
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Extended r-central Bell polynopmials with umbral calculus viewpoint [PDF]
Advances in Difference Equations, 2019 Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were investigated.
Lee-Chae Jang +3 more
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Quantum mechanics and umbral calculus [PDF]
Journal of Physics: Conference Series, 2008 In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions ...
E. Lopez-Sendino +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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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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A note on some identities of derangement polynomials [PDF]
Journal of Inequalities and Applications, 2018 The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255–258, 1978, Clarke and Sved in Math. Mag. 66(5):299–303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):
Taekyun Kim +3 more
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An infinite dimensional umbral calculus [PDF]
Journal of Functional Analysis, 2019 The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of distributions on $\mathbb R^d$, which leads to a general theory of Sheffer polynomial sequences on $\mathcal D'$. We define a sequence of monic polynomials on $\mathcal D'$, a polynomial sequence of binomial type, and a Sheffer sequence.
Dmitri Finkelshtein +3 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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Baxter Algebras and Umbral Calculus [PDF]
, 2004 We apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that include the classical umbral calculus in a family of $ $-umbral calculi parameterized by $ $ in the
Li Guo
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