Results 11 to 20 of about 157,023 (195)
SOME IDENTITIES OF FULLY DEGENERATE DOWLING AND FULLY DEGENERATE BELL POLYNOMIALS ARISING FROM λ-UMBRAL CALCULUS [PDF]
Fractals, 2021 Recently, Kim–Kim introduced the [Formula: see text]-umbral calculus, in which the [Formula: see text]-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and ...
Yuankui Ma +3 more
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Frontiers in Physics, 2013 In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential cornerstones ...
Thomas L Curtright, Cosmas K Zachos
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Two New Generalizations of Extended Bernoulli Polynomials and Numbers, and Umbral Calculus
Journal of Mathematics, 2022 Among a remarkably large number of various extensions of polynomials and numbers, and diverse introductions of new polynomials and numbers, in this paper, we choose to introduce two new generalizations of some extended Bernoulli polynomials and numbers ...
Nabiullah Khan +3 more
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Extended r-central Bell polynopmials with umbral calculus viewpoint
Advances in Difference Equations, 2019 Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were investigated.
Lee-Chae Jang +3 more
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Journal of Mathematical Analysis and Applications, 2000 AbstractIn this paper we establish weaker characteristic conditions of the operator tc and give some new results of invariant operators, basic sequences, and expansion theorem.
Xiehua Sun
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An infinite dimensional umbral calculus [PDF]
Journal of Functional Analysis, 2017 The aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of distributions on $\mathbb R^d$, which leads to a general theory of Sheffer polynomial sequences on $\mathcal D'$. We define a sequence of monic polynomials on $\mathcal D'$, a polynomial sequence of binomial type, and a Sheffer sequence.
D. Finkelshtein +3 more
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Quantum mechanics and umbral calculus [PDF]
Journal of Physics: Conference Series, 2008 In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions ...
E. Lopez-Sendino +3 more
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Formal Calculus and Umbral Calculus [PDF]
The Electronic Journal of Combinatorics, 2010 We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a ...
Thomas J. Robinson
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A note on some identities of derangement polynomials. [PDF]
J Inequal Appl, 2018 The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255–258, 1978, Clarke and Sved in Math. Mag. 66(5):299–303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):
Kim T, Kim DS, Jang GW, Kwon J.
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Journal of Mathematical Analysis and Applications, 1981 AbstractAn algebraic setting for the Roman-Rota umbral calculus is introduced. It is shown how many of the umbral calculus results follow simply by introducing a comultiplication map and requiring it to be an algebra map. The same approach is used to construct a q-umbral calculus.
Edwin Ihrig, Mourad E. H. Ismail
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