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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{
Kim Taekyun, Kim Dae San, Park Jin-Woo
doaj   +3 more sources

Probabilistic degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
Recently, 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, Taekyun Kim, Dae San Kim, Yuankui Ma   +3 more
doaj   +4 more sources

Degenerate Fubini-Type Polynomials and Numbers, Degenerate Apostol–Bernoulli Polynomials and Numbers, and Degenerate Apostol–Euler Polynomials and Numbers

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 ...
Siqintuya Jin, Muhammet Cihat Dağli, Feng Qi   +2 more
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Some identities related to degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
The 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, Wonjoo Kim, Jongkyum Kwon   +3 more
doaj   +4 more sources

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.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
doaj   +3 more sources

Probabilistic identities involving fully degenerate Bernoulli polynomials and degenerate Euler polynomials

Applied Mathematics in Science and Engineering
Assume 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, Jongkyum Kwon
doaj   +4 more sources

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, Dae San Kim, Jongkyum Kwon, Hyunseok Lee   +3 more
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Analytical properties of type 2 degenerate poly-Bernoulli polynomials associated with their applications

Advances in Difference Equations, 2021
Recently, Kim et al. (Adv. Differ. Equ. 2020:168, 2020) considered the poly-Bernoulli numbers and polynomials resulting from the moderated version of degenerate polyexponential functions. In this paper, we investigate the degenerate type 2 poly-Bernoulli
Waseem A. Khan, Ghulam Muhiuddin, Abdulghani Muhyi, Deena Al-Kadi   +3 more
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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
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Explicit relations on the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials and numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
The main aim of this paper is to introduce and investigate the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials by using monomiality principle and operational methods.
Burak Kurt
doaj   +1 more source