A numerical investigation of the roots of q-polynomials

Abstract

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.

Keywords:

• q-Bernoulli numbers
• q-Bernoulli polynomial
• q-Volkenborn integration
• Non-Archimedean analysis
• p-adic valued Bernoulli distribution