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

Abstract EN

We observe the behavior of roots of the (h,q)-extension of Bernoulli polynomials Bn,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 Bn,q(h)(x).

The main purpose of this paper is also to investigate the zeros of the (h,q)-extension of Bernoulli polynomials Bn,q(h)(x).

Furthermore, we give a table for the zeros of the (h,q)-extension of Bernoulli polynomials Bn,q(h)(x).