• Journal of the Korean Mathematical Society
• /
• v.40 no.6
• /
• pp.963-975
• /
• 2003

The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.

• Journal of applied mathematics & informatics
• /
• v.36 no.1_2
• /
• pp.29-38
• /
• 2018

In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

• Honam Mathematical Journal
• /
• v.33 no.4
• /
• pp.519-527
• /
• 2011

Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

• Honam Mathematical Journal
• /
• v.41 no.4
• /
• pp.781-798
• /
• 2019

This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.49-58
• /
• 2005

In this paper we observe the structure of the roots of q-Bernoulli polynomials, ${\beta}_n(w,h{\mid}q)$, using numerical investigation. By numerical experiments, we demonstrate a remarkably regular structure of the real roots of ${\beta}_n(w,h{\mid}q)$ for $-{\frac{1}{5}},-{\frac{1}{2}}$. Finally, we give a table for numbers of real and complex zeros of ${\beta}_n(w,h{\mid}q)$.

• Journal of applied mathematics & informatics
• /
• v.38 no.1_2
• /
• pp.145-157
• /
• 2020

In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1179-1192
• /
• 2018

Several addition formulas for a general class of q-Appell sequences are proved. The q-addition formulas, which are derived, involved not only the generalized q-Bernoulli, the generalized q-Euler and the generalized q-Genocchi polynomials, but also the q-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some q-umbral calculus generalizations of the addition formulas are also investigated.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.575-583
• /
• 2010

In this paper, new q-analogs of Genocchi numbers and polynomials are defined. Some important arithmetic and combinatoric relations are given, in particular, connections with q-Bernoulli numbers and polynomials are obtained.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.601-609
• /
• 2020

In this paper, we introduce degenerate generalized poly-Bernoulli numbers and polynomials with (p, q)-logarithm function. We find some identities that are concerned with the Stirling numbers of second kind and derive symmetric identities by using generalized falling factorial sum.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.315-326
• /
• 2021

Korobov type polynomials are introduced and extensively investigated many mathematicians ([1, 8-10, 12-14]). In this work, we define unified Apostol Korobov type polynomials and give some recurrences relations for these polynomials. Further, we consider the q-poly Korobov polynomials and the q-poly-Korobov type Changhee polynomials. We give some explicit relations and identities above mentioned functions.