Asymptotic distribution of zeros of polynomials satisfying difference equations. (English) Zbl 1019.33008
The author investigates the asymptotic distribution of zeros of orthogonal polynomials satisfying a certain difference equation. In an extensive introduction a survey on the results in this domain is given. Section 2 deals with this method (using the so-called “Bethe Ansatz”) in case of polynomials satisfying a second order differential equation. The sections 3 and 4 deal with polynomials satisfying a difference equation and which are orthogonal with respect to a continuous resp. discrete weight function. In particular the Meixner-Pollaczek polynomials, resp. the Meixner and the Charlier polynomials are considered.
Reviewer: H.-J.Glaeske (Jena)
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 26C10 | Real polynomials: location of zeros |
References:
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