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

Abstract

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 β n , q r and q-Bernoulli polynomials β n , q r ( x ) . We study the q-Bernoulli polynomials β n , q r ( x ) and investigate the roots of the q-Bernoulli polynomials β n , q r ( x ) for values of the index n by using computer. Finally, we consider the reflection symmetries of the q-Bernoulli polynomials.