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Asymptotic normality of the coefficients of polynomials related to the classical system orthogonal ones

✍ Scribed by A. Kyriakoussis; M.G. Vamvakari

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
172 KB
Volume
205
Category
Article
ISSN
0012-365X

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✦ Synopsis

Suitable transformations on the classical system of orthogonal polynomials lead to polynomials with nonnegative coe cients. Asymptotic normality of those coe cients is established by local limit theorem. Applications include, important combinatorial numbers, as the number of connections of a telephone exchange, the coe cients of a rook polynomial, the coe cients of the card matching polynomial and others. Asymptotic formulas for such numbers are also provided whenever it is possible.

πŸ“œ SIMILAR VOLUMES

Asymptotic Behaviour of Orthogonal Polyn
Asymptotic Behaviour of Orthogonal Polynomials on the Unit Circle with Asymptotically Periodic Reflection Coefficients: II. Weak Asymptotics
✍ Franz Peherstorfer; Robert Steinbauer πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 192 KB

In this paper we study orthogonal polynomials with asymptotically periodic reflection coefficients. It's known that the support of the orthogonality measure of such polynomials consists of several arcs. We are mainly interested in the asymptotic behaviour on the support and derive weak convergence r