Results 51 to 60 of about 157,023 (195)
A symbolic method for k-statistics [PDF]
, 2005 Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U-statistics. In addition such a symbolic method can be naturally extended to multivariate case and to generalized k ...
Di Nardo, E., Senato, D.
core +2 more sources
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
core +1 more source
The theory of the umbral calculus III
Journal of Mathematical Analysis and Applications, 1982 Developpement du calcul symbolique des puissances et de la methode des coalgebres et des comodules associee. Application a l'etude des fonctions speciales classiques (hypergeometriques, de Laguerre-Sonine, d'Hermite-Weber, de Legendre et de Bessel)
openaire +4 more sources
Operator Ordering and Solution of Pseudo-Evolutionary Equations
Axioms, 2019 The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary differential ...
Nicolas Behr +2 more
doaj +1 more source
Computer algebra and Umbral Calculus
Discrete Mathematics, 1998 AbstractRota's Umbral Calculus uses sequences of Sheffer polynomials to count certain combinatorial objects. We review this theory and some of its generalizations in light of our computer implementation (Maple V.3). A Mathematica version of this package is being developed in parallel.
A. Bottreau +2 more
openaire +3 more sources
Representations of degenerate poly-Bernoulli polynomials
Journal of Inequalities and Applications, 2021 As is well known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate versions of such functions and polynomials, degenerate polylogarithm functions were introduced and degenerate poly-Bernoulli polynomials
Taekyun Kim +3 more
doaj +1 more source
Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Journal of Mathematics, 2022 Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
doaj +1 more source
Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice
, 1995 `Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a ...
A Dimakis +24 more
core +2 more sources
Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers
Advances in Difference Equations, 2020 The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers of the first and second kinds.
Taekyun Kim +3 more
doaj +1 more source
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.
openaire +2 more sources