A numerical computation of the structure of the roots of q-Bernoulli polynomials

Over the years, there has been increasing interest in solving mathematical problems with the aid of computers. The main purpose of this paper is to construct new generating functions of q-Bernoulli numbers βn,qr and q-Bernoulli polynomials βn,qr(x). We study the q-Bernoulli polynomials βn,qr(x) and investigate the roots of the q-Bernoulli polynomials βn,qr(x) for values of the index n by using computer. Finally, we consider the reflection symmetries of the q-Bernoulli polynomials.