Results 31 to 40 of about 416 (164)
Operational Methods in the Study of Sobolev-Jacobi Polynomials
Mathematics, 2019 Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-called ...
Nicolas Behr +4 more
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λ-q-Sheffer sequence and its applications
Demonstratio Mathematica, 2022 Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ-Sheffer sequence. The purpose of this article is to study λ-q-Sheffer sequence and the degenerate q-Sheffer sequence, which are derived from the ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Open Mathematics, 2023 Hyperharmonic numbers were introduced by Conway and Guy (The Book of Numbers, Copernicus, New York, 1996), whereas harmonic numbers have been studied since antiquity.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Universal constructions in umbral calculus [PDF]
, 1998 Modern umbral calculus is steadily approaching maturity, as applications develop in several areas of mathematics.
Nigel Ray
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Formal calculus, umbral calculus, and basic axiomatics of vertex algebras: [PDF]
, 2009 The central subject of this thesis is formal calculus together with certain applications to vertex operator algebras and combinatorics. By formal calculus we mean mainly the formal calculus that has been used to describe vertex operator algebras and ...
Robinson, Thomas J.
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The Electronic Journal of Combinatorics, 2002 We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state ...
A. Di Bucchianico, D. Loeb
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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
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The theory of the umbral calculus III
Journal of Mathematical Analysis and Applications, 1982 Let P denote the commutative algebra of all polynomials in a single variable x with coefficients in a field K (real or complex) of characteristic zero. Let P * be the vector space of all linear functionals on P and the action of a linear functional L on a polynomial P(x) is denoted by \(\).
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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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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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