A numerical investigation of the structure of the roots of \(q\)-Bernoulli polynomials
type: Item
instance of: scholarly article
title: A numerical investigation of the structure of the roots of \(q\)-Bernoulli polynomials
zbMATH Open document ID: 1115.11016
DOI: 10.1007/BF02831969
published in: Journal of Applied Mathematics and Computing
publication date: 2007-04-05T00:00:00Z
review text: The author studies the \(q\)-Bernoulli polynomials \(B_{n,q^r}(x)\) introduced by \textit{T. Kim} [Russ. J. Math. Phys. 11, No. 1, 71--76 (2004; Zbl 1115.11068)]. Some identities for them are given including the reflection symmetry \[ B_{n,q^{-r}}(1-x)=(-1)^nq^{rn-r}B_{n,q^r}(x),\quad n\geq 0. \] Zeros of some of these polynomials are calculated numerically, which leads the author to a conjecture about the location of the zeros.
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 5140488
zbMATH Keywords: \(q\)-Bernoulli polynomials
zbMATH Keywords: reflection symmetry
author: C. S. Ryoo
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02831969
OpenAlex ID: W3003330994
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description: scientific article; zbMATH DE number 5140488