Recurrence relations for Wronskian Laguerre polynomials

Some Relations on Laguerre Matrix Polynomials

The main object of this paper is to give a di erent approach to proof of generating matrix functions for Laguerre matrix polynomials. We also obtain the hypergeometric matrix representations, addition theorem, nite summation formula and an integral representation for Laguerre matrix polynomials. We get the relations between Laguerre, Legendre and Hermite matrix polynomials. We get the generatin...

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.

Linear Recurrence Relations for Graph Polynomials

A sequence of graphs Gn is iteratively constructible if it can be built from an initial labeled graph by means of a repeated fixed succession of elementary operations involving addition of vertices and edges, deletion of edges, and relabelings. Let Gn be a iteratively constructible sequence of graphs. In a recent paper, [27], M. Noy and A. Ribò have proven linear recurrences with polynomial coe...

On the recurrence coefficients of semiclassical Laguerre polynomials

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 Bäcklu...

Asymptotics of Orthogonal Polynomials via Recurrence Relations