Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle

Details Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle

2000-12-29

arxiv.org/abs/math/0012259v2

J. Approx. Theory 110 (2001), 200-228

Mathematics

Classical Analysis and ODEs

27 pages, Latex2e plus AMS packages Fix to Eqs. (2.72) and (2.74)

Scientific paper

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.

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