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