A Note on the -Extension of Bernoulli Numbers and Bernoulli Polynomials

摘要

We observe the behavior of roots of the (ℎ,?)-extension of Bernoulli polynomials ?(ℎ)?,?(?). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials ?(ℎ)?,?(?). The main purpose of this paper is also to investigatethe zeros of the (ℎ,?)-extension of Bernoulli polynomials ?(ℎ)?,?(?). Furthermore, we give a table for the zeros of the (ℎ,?)-extension of Bernoulli polynomials ?(ℎ)?,?(?).