Results 101 to 110 of about 3,259 (178)
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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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
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Some remarks on Rota's umbral calculus
Indagationes Mathematicae (Proceedings), 1978 The purpose of this note is to show that Rota's theory of polynomials of binomial type and more generally of Sheffer polynomials can be generalized to include ``polynomials of negative degree''. This generalization makes it possible to include the theory of factorial series into Rota's theory and thus solve a problem posed by Rota.
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Some comments on Rota's Umbral Calculus
Journal of Mathematical Analysis and Applications, 1980 AbstractRota's Umbral Calculus is put in the context of general Fourier analysis. Also, some shortcuts in the proofs are illustrated and a new characterization of sequences of binomial type is given. Finally it is shown that there are few (classical) orthogonal polynomials of binomial type.
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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 +2 more
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Umbral calculus and Euler polynomials
, 2012 In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related to special polynomials (see[6]).
Kim, Dae San +2 more
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Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems [PDF]
, 2001 Francis Clarke, John Hunton, Nigel Ray
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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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Cellular Signaling Networks Function as Generalized Wiener-Kolmogorov Filters to Suppress Noise
Physical Review X, 2014 Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity.
Michael Hinczewski, D. Thirumalai
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Set maps, umbral calculus, and the chromatic polynomial [PDF]
, 2007 Gus Wiseman
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