Results 1 to 10 of about 166,207 (201)
Degenerate Bell polynomials associated with umbral calculus [PDF]
Journal of Inequalities and Applications, 2020 Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials.
Taekyun Kim +4 more
doaj +4 more sources
Umbral Calculus in Positive Characteristic [PDF]
arXiv, 2004 An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous $\mathbb F_q$-linear functions are constructed.
Anatoly N. Kochubei
arxiv +7 more sources
Some identities of fully degenerate Dowling and fully degenerate Bell polynomials arising from lambda-umbral calculus [PDF]
Fractals, 2021 Recently, Kim-Kim introduced the lambda-umbral calculus, in which the lambda-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate some properties and identities relating to those polynomials with the help oflambda-umbral calculus.
Yuankui Ma +3 more
arxiv +4 more sources
Degenerate Catalan-Daehee numbers and polynomials of order r arising from degenerate umbral calculus
AIMS Mathematics, 2022 Many mathematicians have studied degenerate versions of some special polynomials and numbers that can take into account the surrounding environment or a person's psychological burden in recent years, and they've discovered some interesting results ...
Hye Kyung Kim, Dmitry V. Dolgy
doaj +3 more sources
Umbral Calculus and the Frobenius-Euler Polynomials [PDF]
Abstract and Applied Analysis, 2013 We study some properties of umbral calculus related to the Appell sequence. From those properties, we derive new and interesting identities of the Frobenius-Euler polynomials.
Dae San Kim, Taekyun Kim, Sang-Hun Lee
doaj +5 more sources
Baxter Algebras and Umbral Calculus [PDF]
Adv. in Appl. Math. 27 (2001), 405-426, 2004 We 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 Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that include the classical umbral calculus in a family of $\lambda$-umbral calculi parameterized by ...
Li Guo
arxiv +5 more sources
Study of degenerate derangement polynomials by λ-umbral calculus
Demonstratio Mathematica, 2023 In the 1970s, Rota began to build completely rigid foundations for the theory of umbral calculus based on relatively modern ideas of linear functions and linear operators.
Yun Sang Jo, Park Jin-Woo
doaj +2 more sources
Some identities of degenerate higher-order Daehee polynomials based on λ-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, Jongkyum Kwon
doaj +2 more sources
On Degenerate Poly-Daehee Polynomials Arising from Lambda-Umbral Calculus
Journal of Mathematics, 2023 In this article, we derived various identities between the degenerate poly-Daehee polynomials and some special polynomials by using λ-umbral calculus by finding the coefficients when expressing degenerate poly-Daehee polynomials as a linear combination ...
Sang Jo Yun, Jin-Woo Park
doaj +2 more sources
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
doaj +2 more sources