On the Carlitz’s type twisted (p, q)-Euler polynomials and twisted (p, q)-Euler zeta function

Abstract

In this paper we construct Carlitz’s type twisted (p, q)-Euler zeta function. In order to define Carlitz’s type twisted (p, q)-Euler zeta function, we introduce the Carlitz’s type twisted (p, q)-Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz’s type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with Carlitz’s type twisted (p, q)-Euler numbers and polynomials. Finally, we investigate the zeros of the Carlitz’s type twisted (p, q)-Euler polynomials by using computer.