A Note on the(h,q)-Extension of Bernoulli Numbers and Bernoulli Polynomials

摘要

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