On two Dimensional q-Bernoulli and q-Genocchi Polynomials: Properties and location of zeros

Abstract

The main purpose of this paper is to investigate two dimensional generalized Genocchi polynomials based on the q-integers. 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-Genocchi numbers and the q-Genocchi polynomials. We describe the structure of the roots of the q-Genocchi polynomials for values of the index n using a computer.