Results 111 to 120 of about 166,207 (201)

A new discretization of the Euler equation via the finite operator theory [PDF]

Open Communications in Nonlinear Mathematical Physics
We 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, Piergiulio Tempesta   +1 more
doaj   +1 more source

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, B. Germano, K. Gorska, M. R. Martinelli   +3 more
openaire   +3 more sources

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
doaj   +2 more sources

A New Approach to Multivariate q-Euler polynomials by using Umbral calculus [PDF]

Journal of Integer Sequences, Vol. 17 (2014), Article 14.1.2, 2012
In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.
arxiv  

Fully degenerate poly-Bernoulli numbers and polynomials

Open Mathematics, 2016
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
doaj   +1 more source

A note on degenerate Euler polynomials arising from umbral calculus

Journal of Mathematics and Computer Science, 2023
S. S. Lee, J.-W. Park
semanticscholar   +1 more source

The classical umbral calculus and the flow of a Drinfeld module

, 2016
The notion of a flow appears in many areas of mathematics and physics; for example, it is one of the fundamental notions in studying ordinary differential equations. Classically a flow on a set X is a group action of the additive group of the set of real
Nguyen Ngoc Dong Quan
semanticscholar   +1 more source

Some remarks on Rota's umbral calculus

Indagationes Mathematicae (Proceedings), 1978
SummaryIt is shown that Rota's theory of Sheffer polynomials can be generalized to the quotient field of the ring of formal power series in 1x. As a special case we give some applications to the classical theories of factorial series and of Laguerre polynomials.
openaire   +2 more sources

Umbral calculus and Frobenius-Euler polynomials [PDF]

arXiv, 2012
In this paper, we study some properties of umbral calculus related to Appell sequence. From those properties, we derive new and interesting identities of Frobenius-Euler polynomials.
arxiv  

The classical umbral calculus: Sheffer sequences

, 2008
Following the approach of Rota and Taylor \cite{SIAM}, we present an innovative theory of Sheffer sequences in which the main properties are encoded by using umbrae. This syntax allows us noteworthy computational simplifications and conceptual clarifications in many results involving Sheffer sequences.
DI NARDO, Elvira, H. NIEDERHAUSEN, D. SENATO   +2 more
openaire   +3 more sources