Results 81 to 90 of about 187 (96)

Type 2 Degenerate Poly-Euler Polynomials

Symmetry, 2020
In recent years, many mathematicians have studied the degenerate versions of many special polynomials and numbers. The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithms functions.
Kim Hye Kyung, Jang Lee-Chae, Hye Kyung Kim   +2 more
exaly   +2 more sources

Some Identities on Type 2 Degenerate Bernoulli Polynomials of the Second Kind

Symmetry, 2020
In recent years, many mathematicians studied various degenerate versions of some special polynomials for which quite a few interesting results were discovered. In this paper, we introduce the type 2 degenerate Bernoulli polynomials of the second kind and
Taekyun Kim, Dae San Kim, Han Young Kim   +2 more
exaly   +2 more sources

Degenerate Bernoulli polynomials, generalized factorial sums, and their applications

Journal of Number Theory, 2008
We prove a general symmetric identity involving the degenerate Bernoulli polynomials and sums of generalized falling factorials, which unifies several known identities for Bernoulli and degenerate Bernoulli numbers and polynomials.
Paul Thomas Young
exaly   +2 more sources

Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials

Symmetry, 2019
In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain p-adic invariant integrals on Z p .
Dmitry V Dolgy, Dae San Kim, Jongkyum Kwon   +2 more
exaly   +2 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   +2 more
exaly   +2 more sources

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
exaly   +2 more sources

Note on Type 2 Degenerate q-Bernoulli Polynomials

Symmetry, 2019
The purpose of this paper is to introduce and study type 2 degenerate q-Bernoulli polynomials and numbers by virtue of the bosonic p-adic q-integrals.
Dae San Kim, Dmitry V Dolgy, Jongkyum Kwon   +2 more
exaly   +2 more sources

Some Identities of Fully Degenerate Bernoulli Polynomials Associated with Degenerate Bernstein Polynomials

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.
Jeong-Gon Lee, Jang Lee-Chae
exaly   +2 more sources

A Note on Degenerate Euler and Bernoulli Polynomials of Complex Variable

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.
Dae Kim, Taekyun Kim, Hyunseok Lee
exaly   +2 more sources

Probabilistic identities involving fully degenerate Bernoulli polynomials and degenerate Euler polynomials

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
exaly   +2 more sources