Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials

Boelen, Lies; Van Assche, Walter

doi:10.1090/S0002-9939-09-10152-1

Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials
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by Lies Boelen and Walter Van Assche PDF

Proc. Amer. Math. Soc. 138 (2010), 1317-1331 Request permission

Abstract:

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 Painlevé equations.

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