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Mathematics > Complex Variables

arXiv:1812.08601 (math)
[Submitted on 20 Dec 2018 (v1), last revised 25 Sep 2019 (this version, v2)]

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

Authors:Innocent Ndikubwayo
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Abstract:This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence $\{P_i\}_{i=1}^{\infty}$ generated by a three-term recurrence relation $P_i(x)+ Q_1(x)P_{i-1}(x) +Q_2(x) P_{i-2}(x)=0$ with the standard initial conditions $P_{0}(x)=1, P_{-1}(x)=0,$ where $Q_1(x)$ and $Q_2(x)$ are arbitrary real polynomials.
Comments: 10 pages, 6 figures, To appear in Czechoslovak mathematical journal, typos corrected, references added
Subjects: Complex Variables (math.CV)
MSC classes: 12D10 (Primary), 26C10, 30C15 (Secondary)
Cite as: arXiv:1812.08601 [math.CV]
  (or arXiv:1812.08601v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1812.08601

Submission history

From: Innocent Ndikubwayo [view email]
[v1] Thu, 20 Dec 2018 14:31:48 UTC (46 KB)
[v2] Wed, 25 Sep 2019 22:28:41 UTC (319 KB)
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