Browsing by Author "Chen, Yang"
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- A characterization theorem for semi-classical orthogonal polynomials on non-uniform latticesPublication . Rebocho, M. N.; Filipuk, Galina; Chen, Yang; Branquinho, A.It is proved a characterization theorem for semi-classical orthogonal polynomials on non- uniform lattices that states the equivalence between the Pearson equation for the weight and some systems involving the orthogonal polynomials as well as the functions of the second kind. As a consequence, it is deduced the analogue of the so-called compatibility conditions in the ladder operator scheme. The classical orthogonal polynomials on non- uniform lattices are then recovered under such compatibility conditions, through a closed formula for the recurrence relation coefficients.
- Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptoticsPublication . Rebocho, M. N.; Filipuk, Galina; Chen, YangIn this paper we derive second and third order nonlinear difference equations for one of the recurrence coefficients in the three term recurrence relation of polynomials orthogonal with respect to a modified Laguerre weight. We show how these equations can be obtained from the Backlund transformations of the third Painlevé equation. We also show how to use nonlinear difference equations to derive a few terms in the formal asymptotic expansions in n of the recurrence coefficients.