Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle
Classical Analysis and ODEs
2007-05-23 v2
Abstract
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and -difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle.
Cite
@article{arxiv.math/0012259,
title = {Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle},
author = {Mourad E. H. Ismail and Nicholas S. Witte},
journal= {arXiv preprint arXiv:math/0012259},
year = {2007}
}
Comments
27 pages, Latex2e plus AMS packages Fix to Eqs. (2.72) and (2.74)