Results 11 to 20 of about 101,104 (278)

Bernoulli F-polynomials and Fibo–Bernoulli matrices

Advances in Difference Equations, 2019
In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
doaj   +1 more source

q-Bernoulli numbers and q-Bernoulli polynomials revisited [PDF]

Advances in Difference Equations, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim Taekyun, Lee Byungje, Ryoo Cheon
openaire   +2 more sources

An integral representation and properties of Bernoulli numbers of the second kind [PDF]

, 2013
In the paper, the author establishes an integral representation and properties of Bernoulli numbers of the second kind and reveals that the generating function of Bernoulli numbers of the second kind is a Bernstein function on $(0,\infty)$.Comment: 9 ...
Qi, Feng
core   +1 more source

The Zagier polynomials. Part II: Arithmetic properties of coefficients [PDF]

, 2013
The modified Bernoulli numbers \begin{equation*} B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 \end{equation*} introduced by D. Zagier in 1998 were recently extended to the polynomial case by replacing $B_{r}$ by the Bernoulli
Coffey, Mark W., De Angelis, Valerio, Dixit, Atul, Moll, Victor H., Straub, Armin, Vignat, Christophe   +5 more
core   +2 more sources

Arithmetical properties of double Möbius-Bernoulli numbers

Open Mathematics, 2019
Given positive integers n, n′ and k, we investigate the Möbius-Bernoulli numbers Mk(n), double Möbius-Bernoulli numbers Mk(n,n′), and Möbius-Bernoulli polynomials Mk(n)(x).
Bayad Abdelmejid, Kim Daeyeoul, Li Yan
doaj   +1 more source

Some Identities of the Degenerate Multi-Poly-Bernoulli Polynomials of Complex Variable

Journal of Function Spaces, 2021
In this paper, we introduce degenerate multi-poly-Bernoulli polynomials and derive some identities of these polynomials. We give some relationship between degenerate multi-poly-Bernoulli polynomials degenerate Whitney numbers and Stirling numbers of the ...
G. Muhiuddin, W. A. Khan, U. Duran, D. Al-Kadi   +3 more
doaj   +1 more source

Some identities of special numbers and polynomials arising from p-adic integrals on Zp $\mathbb{Z}_{p}$

Advances in Difference Equations, 2019
In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials, and degenerate type 2 ...
Dae San Kim, Han Young Kim, Sung-Soo Pyo, Taekyun Kim   +3 more
doaj   +1 more source

Some Identities on the q-Bernoulli Numbers and Polynomials with Weight 0

Abstract and Applied Analysis, 2011
Recently, Kim (2011) has introduced the q-Bernoulli numbers with weight α. In this paper, we consider the q-Bernoulli numbers and polynomials with weight α=0 and give p-adic q-integral representation of Bernstein polynomials associated ...
T. Kim, J. Choi, Y. H. Kim
doaj   +1 more source

A Parametric Type of Cauchy Polynomials with Higher Level

Axioms, 2021
There are many kinds of generalizations of Cauchy numbers and polynomials. Recently, a parametric type of the Bernoulli numbers with level 3 was introduced and studied as a kind of generalization of Bernoulli polynomials.
Takao Komatsu
doaj   +1 more source

Ramanujan-Bernoulli numbers as moments of Racah polynomials [PDF]

, 2019
The classical sequence of Bernoulli numbers is known to the the sequence of moments of a family of orthogonal polynomials. Some similar statements are obtained for another sequence of rational numbers, which is similar in many ways to the Bernoulli ...
Chapoton, Frédéric
core   +3 more sources