Results 101 to 110 of about 159,564 (166)
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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An introduction to Umbral Calculus
, 1998 The aim of these lectures is to give an introduction to combinatorial aspects of Umbral Calculus. Seen in this light, Umbral Calculus is a theory of polynomials that count combinatorial objects.
A. Di Bucchianico
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A selected survey of umbral calculus [PDF]
, 1995 We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of magic rules for lowering and raising indices, through its rebirth in the 1970 ...
Loeb, D., Di Bucchianico, A.; id_orcid
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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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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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Compactly supported wavelets through the classical umbral calculus
, 2006 We explore compactly supported scaling functions of wavelet theory by means of classical umbral calculus as reformulated by Rota and Taylor. We set a theory of orthonormal scaling umbra which leads to a very simple and elementary proof of Lawton's ...
SENATO PULLANO, Domenico +1 more
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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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, 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.
Bottreau, A. +2 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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A New Approach to Multivariate q-Euler Polynomials Using the Umbral Calculus
, 2014 We derive numerous identities for multivariate q- Euler polynomials by using the umbral ...
Araci, Serkan +3 more
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