Results 31 to 40 of about 27,298 (248)

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

Advances in Difference Equations, 2011
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Kim Taekyun, Lee Byungje, Ryoo Cheon
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, Kim Dae San, Dolgy Dmitry V., Park Jin-Woo   +3 more
doaj   +1 more source

A Note on Symmetric Properties of the Twisted q-Bernoulli Polynomials and the Twisted Generalized q-Bernoulli Polynomials

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, H. Yi, K. Shivashankara, T. Kim, Y. H. Kim, B. Lee   +5 more
doaj   +1 more source

Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials [PDF]

, 2013
In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for Genocchi polynomials.
Acikgoz, Mehmet, Araci, Serkan, Şen, Erdoğan   +2 more
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, Dansan 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

Bernoulli-Fibonacci Polynomials

, 2020
By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and numbers are studied in parallel with usual Bernoulli counterparts.
Pashaev, Oktay K., Ozvatan, Merve
openaire   +2 more sources

A note on q-Bernoulli numbers and polynomials [PDF]

, 2005
By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.Comment: 8 ...
Barnes E W, Carlitz L, Kim T, Kim T, Kim T, Kim T, Kim T, Koblitz N, Kurokawa N, Matsumoto K, Nishizawa M, Ota K, Ruijsenaars S N M, Ryoo C S, Ryoo C S, Satoh J, Simsek Y, Srivastava H M, Tsumura H   +18 more
core   +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