Results 31 to 40 of about 325,732 (181)
Applications of Umbral Calculus Associated with p-Adic Invariant Integrals on Zp [PDF]
Abstract and Applied Analysis, 2012 Recently, Dere and Simsek (2012) have studied the applications of umbral algebra to some special functions. In this paper, we investigate some properties of umbral calculus associated with p-adic invariant integrals on Zp.
Dae San Kim, Taekyun Kim
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Journal of Mathematical Analysis and Applications, 2000 The author establishes some weaker characteristic conditions of the operator \(t_c\) and investigates invariant operators. It is shown that if an operator \(T\) can commute with one of the operators \(\sigma_p\) (\(p\neq 0\) and a root of unity), then \(T\) is an invariant operator.
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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. To maximize this utility it is important to work in the most general (as opposed to the most abstract) setting.
Nigel Ray
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An application of the umbral calculus [PDF]
Journal of Mathematical Analysis and Applications, 1990 AbstractThe partial difference equation r(i, j) = r(i, j − 1) + r(i − 1, j) + r(i − 1, J + 1), where r(i, j) are defined for integer numbers i and j, i ⩾ 0, by the conditions r(0, j) = 1 for all j and r(i, −1) = 0 for i ⩾ 1 is solved. For i ⩾ 0 and j ⩾ 0 a combinatorial meaning of numbers r(i, j) is given.
Razpet, Marko
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Some comments on Rota's Umbral Calculus [PDF]
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.
Zeilberger, Doron
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Ultrametric umbral calculus in characteristic $p$
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Identities of Degenerate Poly-Changhee Polynomials Arising from λ-Sheffer Sequences
Journal of Mathematics, 2022 In the 1970s, Gian-Carlo Rota constructed the umbral calculus for investigating the properties of special functions, and by Kim-Kim, umbral calculus is generalized called λ-umbral calculus.
Sang Jo Yun, Jin-Woo Park
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Some identities of degenerate higher-order Daehee polynomials based on $ \lambda $-umbral calculus
Electronic Research Archive, 2023 The degenerate versions of special polynomials and numbers, initiated by Carlitz, have regained the attention of some mathematicians by replacing the usual exponential function in the generating function of special polynomials with the degenerate ...
Dojin Kim, Sangbeom Park, J. Kwon
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A note on infinite series whose terms involve truncated degenerate exponentials
Applied Mathematics in Science and Engineering, 2023 The degenerate exponentials are degenerate versions of the ordinary exponential and the truncated degenerate exponentials are obtained from the Taylor expansions of them by truncating the first finitely many terms.
Dae San Kim, Hyekyung Kim, Taekyun Kim
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