Results 151 to 160 of about 4,745 (169)

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.
D S Kim, Hyunseok Lee
exaly   +3 more sources

ON DEGENERATE q-BERNOULLI POLYNOMIALS

Bulletin of the Korean Mathematical Society, 2016
exaly   +3 more sources

Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials [PDF]

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 . In particular, we derive various expressions for the polynomials associated with integer power sums, called integer power sum polynomials and also ...
D S Kim, Jongkyum Kwon, Taekyun 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. The obtained results are, among other things, several expressions for those polynomials, identities involving those numbers, identities regarding Carlitz’s q-Bernoulli numbers, identities concerning ...
D S Kim, Jongkyum Kwon, Taekyun Kim
exaly   +2 more sources

Some of the next articles are maybe not open access.

Related searches:

CLOSED FORMS FOR DEGENERATE BERNOULLI POLYNOMIALS

Bulletin of the Australian Mathematical Society, 2020
Qi and Chapman [‘Two closed forms for the Bernoulli polynomials’, J. Number Theory159 (2016), 89–100] gave a closed form expression for the Bernoulli polynomials as polynomials with coefficients involving Stirling numbers of the second kind. We extend the formula to the degenerate Bernoulli polynomials, replacing the Stirling numbers by degenerate ...
Dai, Lei, Pan, Hao
openaire   +2 more sources

Some Identities of Carlitz Degenerate Bernoulli Numbers and Polynomials [PDF]

Iranian Journal of Science and Technology, Transaction A: Science, 2017
In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.
D S Kim, Taekyun Kim
exaly   +4 more sources

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

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 their higher-order analogues, and study some identities and expressions for these polynomials ...
D S Kim
exaly   +3 more sources

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, Wonjoo Kim, Lee-Chae Jang
exaly   +3 more sources

Degenerate Versions of Hypergeometric Bernoulli–Euler Polynomials

Lobachevskii Journal of Mathematics
In this paper, we introduce degenerate versions of the hypergeometric Bernoulli and Euler polynomials. We demonstrate that they form Δλ-Appell sets and provide some of their algebraic properties, including inversion formulas, as well as the associated matrix formulation.
Yamilet Quintana, William Ramirez
exaly   +3 more sources