On the recurrence coefficients of semiclassical Laguerre polynomials
نویسندگان
چکیده
It is known [L. Boelen, W. Van Assche, Proc. Amer. Math. Soc. 138 (2010), 1317–1331] that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semiclassical extension of the Laguerre weight satisfy a discrete Painlevé equation. By using the Toda system for the recurrence coefficients we show that this discrete equation can be obtained from a Bäcklund transformation of the fourth Painlevé equation.
منابع مشابه
Discrete Painlevé Equations for Recurrence Coefficients of Semiclassical Laguerre Polynomials
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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