Results 1 to 10 of about 144 (134)
The Umbral Calculus of Symmetric Functions
Advances in Mathematics, 1996 The author develops an umbral calculus for the symmetric functions in an infinite number of variables. This umbral calculus is analogous to Roman-Rota umbral calculus for polynomials in one variable, see \textit{S. M. Roman} and \textit{G.-C. Rota} [Adv. Math. 27, 95-188 (1978; Zbl 0375.05007)].
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Recursive matrices and umbral calculus
Journal of Algebra, 1982 Two major objectives can be seen to guide much recent work in enumeration: (1) to single out a limited variety of recurrences for numerical sequences which will encompass counting problems of wide-enough type; (2) to recover from empirical data an underlying set-theoretic structure which would reveal the source of the given recursion.
Barnabei, Marilena +2 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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Integration in the umbral calculus
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.”
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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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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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A new discretization of the Euler equation via the finite operator theory [PDF]
Open Communications in Nonlinear Mathematical PhysicsWe propose a novel discretization procedure for the classical Euler equation, based on the theory of Galois differential algebras and the finite operator calculus developed by G.C. Rota and collaborators.
Miguel A. Rodríguez +1 more
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An application of the umbral calculus
Journal of Mathematical Analysis and Applications, 1990 AbstractThe partial difference equation r(i, j) = r(i, j − 1) + r(i − 1, j) + r(i − 1, J + 1), where r(i, j) are defined for integer numbers i and j, i ⩾ 0, by the conditions r(0, j) = 1 for all j and r(i, −1) = 0 for i ⩾ 1 is solved. For i ⩾ 0 and j ⩾ 0 a combinatorial meaning of numbers r(i, j) is given.
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Can Umbral and q-calculus be merged?
, 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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Approximation operators constructed by means of Sheffer sequences
Journal of Numerical Analysis and Approximation Theory, 2001 In this paper we introduce a class of positive linear operators by using the "umbral calculus", and we study some approximation properties of it. Let \( Q \) be a delta operator, and \(S\) an invertible shift invariant operator. For \(f\in C[0,1]\) we
Maria Crăciun
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