2000/12/31 by Mourad E. H. Ismail, Nicholas S. Witte
Mathematics · #math.CA #msc:42C05 #msc:33C45
published as J. Approx. Theory 110 (2001), 200-228 · 27 pages, Latex2e plus AMS packages Fix to Eqs. (2.72) and (2.74)
arxiv created 2001/08/01 · arxiv updated 2009/11/30
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and q-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.