A Note on the (ℎ,𝑞)-Extension of Bernoulli Numbers and Bernoulli Polynomials - C. S. Ryoo; T. Kim (Discrete Dynamics in Nature and Society)
We observe the behavior of roots of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). The main purpose of this paper is also to investigate the zeros of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). Furthermore, we give a table for the zeros of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥).