| Автор | Chie Bing Wang |
| Дата выпуска | 1999-10-15 |
| dc.description | We consider the polynomials <sub>n</sub>(z) = <sub>n</sub>(z<sup>n</sup>+b<sub>n-1</sub>z<sup>n-1</sup>+...) orthonormal with respect to the weight exp(()<sup>1/2</sup>(z+1/z)) dz/2iz on the unit circle in the complex plane. The leading coefficient <sub>n</sub> is found to satisfy a difference-differential (spatially discrete) equation which is further proved to approach a third-order differential equation by double scaling. The third-order differential equation is equivalent to the Painlevé II equation. The leading coefficient and second leading coefficient of <sub>n</sub>(z) can be expressed asymptotically in terms of the Painlevé II function. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Orthonormal polynomials on the unit circle and spatially discrete PainlevéII equation |
| Тип | paper |
| DOI | 10.1088/0305-4470/32/41/312 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 32 |
| Первая страница | 7207 |
| Последняя страница | 7217 |
| Аффилиация | Chie Bing Wang; Department of Mathematics and Institute of Theoretical Dynamics University of California, Davis, CA 95616, USA |
| Выпуск | 41 |
