Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation

TitleCriterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation
Publication TypeJournal Article
Year of Publication2020
AuthorsNdikubwayo, I
JournalCzechoslovak Mathematical
Volume 70
Pagination793–804
Abstract

Abstract. This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence {Pi}∞i=1 generated by a three-term recurrence relation Pi(x)+Q1(x)Pi−1(x)+Q2(x)Pi−2(x) = 0 with the standard initial conditions P0(x) = 1, P−1(x) = 0, where Q1(x) and Q2(x) are arbitrary real polynomials. 

URLhttps://arxiv.org/pdf/1812.08601.pdf