Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902714 | Applied Numerical Mathematics | 2018 | 13 Pages |
Abstract
In this paper we study families of semi-classical orthogonal polynomials within class one. We derive general second or third order ordinary differential equations (with respect to certain parameters) for the recurrence coefficients of the three-term recurrence relation of these polynomials and show that in particular well-known cases, e.g. related to the modified Airy and Laguerre weights, these equations can be reduced to the second and the fourth Painlevé equations.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
G. Filipuk, M.N. Rebocho,