DISCRETE PAINLEVÉ EQUATIONS FOR RECURRENCE COEFFICIENTS OF SEMICLASSICAL LAGUERRE POLYNOMIALS

By Lies Boelen, Walter Van Assche. 2010

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We consider two semiclassical extensions of the Laguerre weight and their associated sets of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the coefficients appearing in this relation satisfy discrete Painleve equations.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d1d3f6fee8baf45d0e95c1b95c4206e4d15c0e2b