| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 366.78 KB | Adobe PDF |
Advisor(s)
Abstract(s)
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.
Description
Keywords
Painlev e equations Semi-classical orthogonal polynomials Stieltjes function
Citation
G. Filipuk and M.N. Rebocho, Differential equations for families of semi- classical orthogonal polynomials within class one, Applied Numerical Mathematics 124 (2018) 76-88.