Monday, January 14, 2013

1301.2401 (Nobutaka Nakazono)

Solutions to discrete Painlevé systems arising from two types of
orthogonal polynomials (I)

Nobutaka Nakazono
We consider the relation between discrete Painlev\'e systems and orthogonal polynomials associated with the Christoffel transformation. We construct a method to obtain the particular solutions to discrete Painlev\'e systems by using orthogonal polynomials and their kernel polynomials. In particular, we treat the cases of the Hermite polynomials and the discrete $q$-Hermite II polynomials as examples.
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