Seog-Hoon Rim

The twisted Daehee numbers and polynomials

We consider the Witt-type formula for the n th twisted Daehee numbers and polynomials and investigate some properties of those numbers and polynomials. In particular, the n th twisted Daehee numbers are closely related to higher-order Bernoulli numbers and Bernoulli numbers of the second kind.

ON THE ANALOGS OF BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND ZETA AND L-FUNCTIONS

In this paper, by using q-deformed bosonic p-adic integral, we give -Bernoulli numbers and polynomials, we prove Witts type formula of -Bernoulli polynomials and Gauss multiplicative formula for -Bernoulli polynomials. By using derivative operator to the generating functions of -Bernoulli polynomials and generalized -Bernoulli numbers, we give Hurwitz type -zeta functions and Dirichlets type -L-functions; which are interpolated -Bernoulli polynomials and generalized -Bernoulli numbers, respectively. We give generating function of -Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and -Bernoulli polynomials and ordinary Bernoulli numbers of order r and -Bernoulli numbers, respectively. We also study on -Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define -partial zeta function and interpolation function.

On Genocchi Numbers and Polynomials

The main purpose of this paper is to study the distribution of Genocchi polynomials. Finally, we construct the Genocchi zeta function which interpolates Genocchi polynomials at negative integers.

On the twisted q-Euler numbers and polynomials associated with basic q-l-functions

One of the purposes of this paper is to construct the twisted q-Euler numbers by using p-adic invariant integral on Zp in the fermionic sense. Moreover, we consider the twisted Euler q-zeta functions and q-l-functions which interpolate the twisted q-Euler numbers and polynomials at a negative integer.

Exploring the q-Riemann zeta function and q-Bernoulli polynomials

We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to βs(z). A new formula for the q-Riemann zeta function ζq(s) due to Kim in terms of nested series of ζq(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of “scattering” of the zeros of βs(z) is observed. Following the idea of q-zeta function due to Kim, we are going to use “Mathematica” to explore a formula for ζq(n).

Umbral calculus and Sheffer sequences of polynomials

In this paper, we investigate some properties of Sheffer sequences of polynomials arising from umbral calculus. From these properties, we derive new and interesting identities between Sheffer sequences of polynomials. An application to normal ordering is presented.

Some Identities on the Twisted h, q -Genocchi Numbers and Polynomials Associated with q-Bernstein Polynomials

We give some interesting identities on the twisted (ℎ,𝑞)-Genocchi numbers and polynomials associated with 𝑞-Bernstein polynomials.

A note on q-Euler numbers associated with the basic q-zeta function

Abstract The purpose of this work is to give some identities of q -Euler numbers and polynomials. Finally we construct q -zeta functions which interpolate the q -analogue of Frobenius–Euler numbers at negative integers.

New Approach to q-Euler Numbers and Polynomials

We give a new construction of the Open image in new window-extensions of Euler numbers and polynomials. We present new generating functions which are related to the Open image in new window-Euler numbers and polynomials. We also consider the generalized Open image in new window-Euler polynomials attached to Dirichlets character Open image in new window and have the generating functions of them. We obtain distribution relations for the Open image in new window-Euler polynomials and have some identities involving Open image in new window-Euler numbers and polynomials. Finally, we derive the Open image in new window-extensions of zeta functions from the Mellin transformation of these generating functions, which interpolate the Open image in new window-Euler polynomials at negative integers.

Frobenius-Euler polynomials and umbral calculus in the p-adic case

In this paper, we study some p-adic Frobenius-Euler measure related to umbral calculus in the p-adic case. Finally, we derive some identities of Frobenius-Euler polynomials from our study.MSC:05A10, 05A19.