A general explicit first and second order differential equation, plus a Verblunsky-coefficient difference equation, is established for semiclassical orthogonal polynomials on the unit circle with Pearson weights of degree at most three.
Specifically, we consider and generalize some of the weight functions that were characterized in [4] to illustrate applications of Theorems 3.1, 3.6, and Corollary 3.7
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Differential equations for a class of semiclassical orthogonal polynomials on the unit circle
A general explicit first and second order differential equation, plus a Verblunsky-coefficient difference equation, is established for semiclassical orthogonal polynomials on the unit circle with Pearson weights of degree at most three.