Strong asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight
| dc.creator | Vanlessen, M. | |
| dc.date | 2002-12-02 | |
| dc.date.accessioned | 2026-07-07T04:53:26Z | |
| dc.date.available | 2026-07-07T04:53:26Z | |
| dc.description | We study asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight, which is a weight function with a finite number of algebraic singularities on $[-1,1]$. The recurrence coefficients can be written in terms of the solution of the corresponding Riemann-Hilbert problem for orthogonal polynomials. Using the steepest descent method of Deift and Zhou, we analyze the Riemann-Hilbert problem, and obtain complete asymptotic expansions of the recurrence coefficients. We will determine explicitly the order $1/n$ terms in the expansions. A critical step in the analysis of the Riemann-Hilbert problem will be the local analysis around the algebraic singularities, for which we use Bessel functions of appropriate order. | |
| dc.description | 31 pages, 6 figures, 21 references | |
| dc.identifier | https://arxiv.org/abs/math/0212014 | |
| dc.identifier | http://arxiv.org/abs/math/0212014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65852 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 30E25; 33C10; 42C05 | |
| dc.title | Strong asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight | |
| dc.type | text |