Results 41 to 50 of about 3,259 (178)
Dual Numbers and Operational Umbral Methods
Axioms, 2019 Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view,
Nicolas Behr +3 more
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Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering [PDF]
, 2005 We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1 in terms of ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link between the monomiality principle and the umbral calculus.
Blasiak, P +3 more
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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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Computer algebra and Umbral Calculus
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Bottreau +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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Recursive matrices and umbral calculus
Journal of Algebra, 1982 Two major objectives can be seen to guide much recent work in enumeration: (1) to single out a limited variety of recurrences for numerical sequences which will encompass counting problems of wide-enough type; (2) to recover from empirical data an underlying set-theoretic structure which would reveal the source of the given recursion.
Andrea Brini +2 more
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Representations of degenerate poly-Bernoulli polynomials
Journal of Inequalities and Applications, 2021 As is well known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate versions of such functions and polynomials, degenerate polylogarithm functions were introduced and degenerate poly-Bernoulli polynomials
Taekyun Kim +3 more
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Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice
, 1995 `Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a ...
A Dimakis +24 more
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