Results 41 to 50 of about 726,471 (254)

On Apostol-Type Hermite Degenerated Polynomials [PDF]

, 2023
This article presents a generalization of new classes of degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials of level m.
Stiven Díaz, Adnan Shamaoon, Díaz , Stiven, Ramirez, William, Cesarano, Clemente, Shamaoon, Adnan, William Ramírez, Waseem Ahmad Khan, Clemente Cesarano, Khan, Waseem A.   +9 more
core   +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

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, Dae San Kim, Han-Young Kim, Hyunseok Lee, Lee-Chae Jang   +4 more
doaj   +1 more source

A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function

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

Generalized harmonic numbers via poly-Bernoulli polynomials [PDF]

, 2020
Harmonic numbers and some of their generalizations are related to Bernoulli numbers and polynomials. In this paper, we present a connection between generalized hyperharmonic numbers and poly-Bernoulli polynomials.
L. Kargin, Mehmet Cenkci, A. Dil, M. Can
semanticscholar   +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, Bai-Ni Guo, Feng Qi, Lokenath Debnath   +3 more
openaire   +2 more sources

Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials with applications to series involving zeros of Bessel functions [PDF]

, 2018
We introduce Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials as generalizations of Bernoulli and Apostol–Euler polynomials, where the role of the derivative is now played by the Dunkl operator on the real line.
Pérez, Mario, Varona, Juan L., Mario Pérez, Durán, A.J. [0000-0002-8351-7392], Óscar Ciaurri, Antonio J. Durán, Varona, J.L. [0000-0002-2023-9946], Ciaurri, Óscar, Pérez, M. [0000-0002-3050-3712], Durán, Antonio J., Ciaurri, Ó. [0000-0002-1695-3311], Juan L. Varona, Ciaurri, Ó., Pérez, M., Durán, A.J., Varona, J.L.   +15 more
core   +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

Fourier Series for the Tangent Polynomials, Tangent–Bernoulli and Tangent–Genocchi Polynomials of Higher Order

Axioms, 2022
In this paper, the Fourier series expansion of Tangent polynomials of higher order is derived using the Cauchy residue theorem. Moreover, some variations of higher-order Tangent polynomials are defined by mixing the concept of Tangent polynomials with ...
Cristina Bordaje Corcino, Roberto Bagsarsa Corcino   +1 more
doaj   +1 more source

On Generalized Bivariate (p,q)-Bernoulli–Fibonacci Polynomials and Generalized Bivariate (p,q)-Bernoulli–Lucas Polynomials

, 2023
Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with the help of generating functions and their functional equations.
Can Kızılateş, Hao Guan, Waseem Ahmad Khan   +2 more
core   +1 more source