On a class of two dimensional (w, q)-Bernoulli and (w, q)-Euler polynomials: Properties and location of zeros

Abstract

The main purpose of this paper is to introduce and investigate two dimensional (w, q)-Bernoulli and (w, q)-Euler polynomials. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava-Pinter addition theorem is obtained. Furthermore we explore the shapes of the q-Bernoulli numbers and the q-Bernoulli polynomials. We describe the structure of the roots of the q-Bernoulli polynomials for values of the index n using a computer.