Results 21 to 30 of about 26,237 (204)
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. +5 more
core +2 more sources
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 +3 more
doaj +1 more source
Degenerate Bell polynomials associated with umbral calculus
Journal of Inequalities and Applications, 2020 Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials.
Taekyun Kim +4 more
doaj +1 more source
Generalizations of Bernoulli numbers and polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a, b) are generalized to the one Bn(x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a, b), and Bn(
Qiu-Ming Luo +3 more
openaire +2 more sources
On the type 2 poly-Bernoulli polynomials associated with umbral calculus
Open Mathematics, 2021 Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques.
Kim Taekyun +3 more
doaj +1 more source
Identities involving Laguerre polynomials derived from umbral calculus [PDF]
, 2013 In this paper, we investigate some identities of Laguerre polynomials involving Bernoulli and Euler polynomials which are derived from umbral calculus.Comment: 12 ...
Kim, Taekyun
core +1 more source
Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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
Degenerate poly-Bernoulli polynomials arising from degenerate polylogarithm
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
doaj +1 more source
Advances in Difference Equations, 2010 We define the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomials attached to χ of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain
L.-C. Jang +5 more
doaj +1 more source