Monotonicity of zeros for a class of polynomials including hypergeometric polynomials

摘要

We study the monotonicity of zeros in connection with perturbed recurrence coefficients of polynomials satisfying certain three-term recurrence relations of Frobenius-type. These recurrence relations are the key ingredient for the tridiagonal approach developed by Delsarte and Genin to solve the standard linear prediction problem. As a particular case, we consider the Askey para-orthogonal polynomials on the unit circle, 2F1(−n,a+bi;2a;1−z),a,b∈R, extending a recent result about the monotonicity of their zeros with respect to the parameter b. Finally, the consequences of our results in the theory of orthogonal polynomials on the real line are discussed.