Name
Abstract | ||
|---|---|---|
In this paper we derive the nonlinear recurrence relation for the recursion coefficients @b"n of polynomials orthogonal with respect to q-analogues of Freud exponential weights. An asymptotic relation for @b"n is given under assuming a certain smoothing condition and the Plancherel-Rotach asymptotic for the corresponding orthogonal polynomials is derived. Special interest is paid to the case m=2. We prove that the nonlinear recurrence relation of @b"n in this case obeys the discrete Painleve property. Motivated by Lew and Quarles, we study possible periodic solutions for a class of nonlinear difference equations of second order. Finally we prove that the Bernstein approximation problem associated to the weights under consideration has a positive solution. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.aam.2010.02.003 | Advances in Applied Mathematics |
Keywords | DocType | Volume |
nonlinear recurrence relation,freud weight,certain smoothing condition,case m,freud exponential weight,nonlinear difference equation,bernstein approximation problem,polynomials orthogonal,asymptotic relation,plancherel-rotach asymptotic,corresponding orthogonal polynomial,difference equation,orthogonal polynomial,second order,recurrence relation | Journal | 45 |
Issue | ISSN | Citations |
4 | 0196-8858 | 0 |
PageRank | References | Authors |
0.34 | 1 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mourad E. H. Ismail | 1 | 75 | 25.95 |
| Z. S. I. Mansour | 2 | 0 | 0.68 |