Results 1 to 10 of about 212 (165)
Probabilistic degenerate Bernoulli and degenerate Euler polynomials
Mathematical and Computer Modelling of Dynamical SystemsRecently, many authors have studied degenerate Bernoulli and degenerate Euler polynomials. Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin.
Lingling Luo +2 more
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Some identities related to degenerate Bernoulli and degenerate Euler polynomials
Mathematical and Computer Modelling of Dynamical SystemsThe aim of this paper is to study degenerate Bernoulli and degenerate Euler polynomials and numbers and their higher-order analogues. We express the degenerate Euler polynomials in terms of the degenerate Bernoulli polynomials and vice versa.
Taekyun Kim, Dae San Kim
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Applied Mathematics in Science and EngineeringAssume that X is the Bernoulli random variable with parameter [Formula: see text], and that random variables [Formula: see text] are a sequence of mutually independent copies of X.
Taekyun Kim, Dae San Kim
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Fully degenerate Bernoulli numbers and polynomials
Demonstratio Mathematica, 2022 The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{
Taekyun Kim +2 more
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Some Identities of Fully Degenerate Bernoulli Polynomials Associated with Degenerate Bernstein Polynomials [PDF]
Symmetry, 2019 In this paper, we investigate some properties and identities for fully degenerate Bernoulli polynomials in connection with degenerate Bernstein polynomials by means of bosonic p-adic integrals on Z p and generating functions. Furthermore, we study two variable degenerate Bernstein polynomials and the degenerate Bernstein operators.
Jeong-Gon Lee, Jang Lee-Chae
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Axioms, 2022 In this paper, by introducing degenerate Fubini-type polynomials, with the help of the Faà di Bruno formula and some properties of partial Bell polynomials, the authors provide several new explicit formulas and recurrence relations for Fubini-type ...
Muhammet Cihat Dagli, Feng Qi
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Fully degenerate poly-Bernoulli numbers and polynomials
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Taekyun Kim +2 more
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Representations of degenerate poly-Bernoulli polynomials [PDF]
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
doaj +3 more sources
Degenerate poly-Bernoulli polynomials arising from degenerate polylogarithm [PDF]
Advances in Difference Equations, 2020 Recently, degenerate polylogarithm functions were introduced by Kim and Kim. In this paper, we introduce degenerate poly-Bernoulli polynomials by means of the degenerate polylogarithm functions and investigate some their properties.
Taekyun Kim +4 more
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A Note on Degenerate Euler and Bernoulli Polynomials of Complex Variable [PDF]
Symmetry, 2019 Recently, the so-called new type Euler polynomials have been studied without considering Euler polynomials of a complex variable. Here we study degenerate versions of these new type Euler polynomials. This has been done by considering the degenerate Euler polynomials of a complex variable.
Dae Kim, Taekyun Kim, Hyunseok Lee
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