So far Bernoulli polynomials, are studied by many people for their interesting properties. Several authors considered different generalizations of  and obtained some analogous properties. Hassen and Nguyen in [10] introduced a generalization of  called hypergeometric Bernoulli polynomials of order N,  These polynomials, when   are given by

For Bernoulli polynomials, Mangual [18] studied about their asymptotic behavior and how the complex zeros of the re-scaled polynomials  behave, for large values of n. After reading what Mangual [18] did for we studied analogous concepts for the polynomials

In this paper, we discuss some asymptotic behavior of  analogous to that of We briefly describe the asymptotic complex zeros of  by presenting a curve to which the zeros are attracted as n goes to infinity.

Bernoulli numbers and polynomials, hypergeometric Bernoulli polynomials, Hurwitz zeta functions, asymptotic zeros.

Received: February 11, 2020; Accepted: April 25, 2020; Published: January 25, 2021

How to cite this article: Nasir Asfaw and Abdul Hassen, Asymptotic behavior and zeros of hypergeometric Bernoulli polynomials of order 2, JP Journal of Algebra, Number Theory and Applications 49(1) (2021), 51-75. DOI: 10.17654/NT049010051

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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