C. S. Ryoo

On the Fermionic -adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials

The purpose of this paper is to give some properties of several Bernstein type polynomials to represent the fermionic -adic integral on . From these properties, we derive some interesting identities on the Euler numbers and polynomials.

Some Relationships between the Analogs of Euler Numbers and Polynomials

We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distribution relations of generalized twisted Euler numbers and polynomials. By numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted-Euler polynomials. Finally, we give a table for the solutions of the twisted-Euler polynomials.

Exploring the multiple Changhee q-Bernoulli polynomials

In this article, we will discuss the behaviour of the roots of the multiple Changhee q-Bernoulli polynomials for values of the index n by using computer.

A numerical investigation of the roots of q-polynomials

In this paper we explore the shapes of the q-numbers K n, q and the q-polynomials K n, q (x). Finally, we describe the structure of the roots of the q-polynomials K n, q (x) for values of the index n using a computer.

On the Generalized -Genocchi Numbers and Polynomials of Higher-Order

We first consider the -extension of the generating function for the higher-order generalized Genocchi numbers and polynomials attached to . The purpose of this paper is to present a systemic study of some families of higher-order generalized -Genocchi numbers and polynomials attached to by using the generating function of those numbers and polynomials.

A Note on the Multiple Twisted Carlitz's Type q-Bernoulli Polynomials

We give the twisted Carlitzs type 𝑞 -Bernoulli polynomials and numbers associated with 𝑝 -adic 𝑞 -inetgrals and discuss their properties. Furthermore, we define the multiple twisted Carlitzs type 𝑞 -Bernoulli polynomials and numbers and obtain the distribution relation for them.

Some Identities of the Twisted -Genocchi Numbers and Polynomials with Weight and -Bernstein Polynomials with Weight

Recently mathematicians have studied some interesting relations between 𝑞-Genocchi numbers, 𝑞-Euler numbers, polynomials, Bernstein polynomials, and 𝑞-Bernstein polynomials. In this paper, we give some interesting identities of the twisted 𝑞-Genocchi numbers, polynomials, and 𝑞-Bernstein polynomials with weighted 𝛼.

Some Identities of Bernoulli Numbers and Polynomials Associated with Bernstein Polynomials

We investigate some interesting properties of the Bernstein polynomials related to the bosonic -adic integrals on .

The twisted (h, q)-Genocchi numbers and polynomials with weight α and q-bernstein polynomials with weight α

In this article, we give some identities on the twisted (h, q)-Genocchi numbers and polynomials and q-Bernstein polynomials with weighted α.

Some Identities on the Generalized -Bernoulli Numbers and Polynomials Associated with -Volkenborn Integrals

We give some interesting equation of -adic -integrals on . From those -adic -integrals, we present a systemic study of some families of extended Carlitz type -Bernoulli numbers and polynomials in -adic number field.