Czechoslovak Mathematical Journal, Vol. 70, No. 3, pp. 793-804, 2020
Criterion of the reality of zeros in a polynomial sequence satisfying a three-term
recurrence relation
Innocent Ndikubwayo
Received December 4, 2018. Published online February 24, 2020.
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.
Keywords: recurrence relation; polynomial sequence; support; real zeros
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Affiliations: Innocent Ndikubwayo, Department of Mathematics, Stockholm University, Kräftriket, SE-106 91 Stockholm, Sweden; Department of Mathematics, Makerere University, P.O Box 7062 Kampala, Uganda, e-mail: innocent@math.su.se, ndikubwayo@cns.mak.ac.ug
