Results 21 to 30 of about 166,207 (201)
A Characterization of Umbral Calculus Inspired by Fractional Sums [PDF]
arXiv, 2021 We will use analytic function theory and Fourier analysis to establish a characterization for some classical umbral calculus, which will focus on the generalization of the evaluation function. Although we cannot cover all the umbral calculus people care about, the part about Bernoulli numbers can still answer an open question about fractional sums ...
Qian Tang
arxiv +3 more sources
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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Bernoulli-Taylor formula for psi-umbral difference calculus [PDF]
arXiv, 2003 An expansion formula of a new type with the rest term of Cauchy type is derived in the operator formulation of generalized umbral ...
A. K. Kwaśniewski
arxiv +3 more sources
Umbral calculus and Euler polynomials [PDF]
arXiv, 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
arxiv +3 more sources
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.
europepmc +2 more sources
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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Applications of the classical umbral calculus [PDF]
Algebra Universalis 49 (2003), 397-434, 2001 We describe applications of the classical umbral calculus to bilinear generating functions for polynomial sequences, identities for Bernoulli and related numbers, and Kummer congruences.
Ira M. Gessel
arxiv +3 more sources
Baxter Algebras and the Umbral Calculus
Advances in Applied Mathematics, 2001 AbstractWe apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of the Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that includes the classical umbral calculus in a family of λ-umbral calculi parameterized by λ
Li Guo
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Applications of the classical umbral calculus [PDF]
Algebra Universalis, 2003 34 ...
Ira M. Gessel
openalex +5 more sources