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.
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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.