A numerical computation of the structure of the roots of q-Bernoulli polynomials

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摘要

Over the years, there has been increasing interest in solving mathematical problems with the aid of computers. The main purpose of this paper is to construct new generating functions of q-Bernoulli numbers βn,qr and q-Bernoulli polynomials βn,qr(x). We study the q-Bernoulli polynomials βn,qr(x) and investigate the roots of the q-Bernoulli polynomials βn,qr(x) for values of the index n by using computer. Finally, we consider the reflection symmetries of the q-Bernoulli polynomials.

论文关键词：11B68,11S40,Bernoulli polynomials,Bernoulli numbers,q-Bernoulli polynomials,q-Bernoulli numbers,Generating functions of q-Bernoulli numbers,Roots of the q-Bernoulli polynomials,Reflection symmetries of the q-Bernoulli polynomials

论文评审过程：Received 4 May 2006, Revised 21 February 2007, Available online 12 March 2007.

论文官网地址：https://doi.org/10.1016/j.cam.2007.02.041