Polynomials generated by a three term recurrence relation: bounds for complex zeros
The authors investigate bounds for the zeros of polynomials \(Q_m(z)\) defined by the three-term recurrence relation \[ Q_{m+1}(z)=(z+\beta_{m+1})Q_m(z)-\alpha_{m+1}zQ_{m-1}(z),\quad m=1,2,\ldots \] with \(Q_0=1\) and \(Q_1(z)=z+\beta_1\), under a variety of assumptions on the complex numbers \(\alpha_m\) and \(\beta_m\) (the results are too technical to be reported here). Applications to Szegö polynomials, para-orthogonal polynomials, and polynomials with non-zero complex coefficients are also discussed.
scientific article; zbMATH DE number 2165364
scientific article