Monotonicity of zeros for a class of polynomials including hypergeometric polynomials Articles uri icon

authors

  • CASTILLO RODRIGUEZ, KENIER

publication date

  • September 2016

start page

  • 183

end page

  • 193

volume

  • 266

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

abstract

  • 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.

keywords

  • three-term recurrence relation; hypergeometric polynomials; zeros; monotonicity