Geodesic
Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 793-804

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MR
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.
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.
DOI : 10.21136/CMJ.2020.0535-18
Classification : 12D10, 26C10, 30C15
Keywords: recurrence relation; polynomial sequence; support; real zeros 
Ndikubwayo, Innocent. Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 793-804. doi: 10.21136/CMJ.2020.0535-18
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