Abstract
This paper investigates the zero distribution of a sequence of polynomials \(\left\{ P_{m}(z)\right\} _{m=0}^{\infty }\) which satisfy a four-term recurrence whose coefficients are linear polynomials in z. In particular, we study necessary and sufficient conditions for the reality of the zeros of \(P_{m}(z)\). Under these conditions, we find an explicit interval containing these zeros, whose union forms a dense subset of this interval.
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Tran, K., Zumba, A. Zeros of polynomials with four-term recurrence and linear coefficients. Ramanujan J 55, 447–470 (2021). https://doi.org/10.1007/s11139-020-00263-0
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DOI: https://doi.org/10.1007/s11139-020-00263-0