Methods and Applications of Analysis

Volume 14 (2007)

Number 1

Asymptotics for Polynomials Satisfying a Certain Twin Asymptotic Periodic Recurrence Relation: Unbounded Cases

Pages: 29 – 44

DOI: http://dx.doi.org/10.4310/MAA.2007.v14.n1.a3

Authors

E.X.L. de Andrade

F.A. Kurokawa

A. Sri Ranga Ranga

Abstract

Polynomials satisfying a certain twin asymptotic periodic recurrence relation are considered. It is assumed that the coefficients of the recurrence formula are unbounded but vary regularly and have different behaviour for even and odd indices. The asymptotic behaviour of the ratio of contiguous polynomials is analyzed.

Keywords

Orthogonal L-polynomials; Stieltjes transforms; three term recurrence relation

2010 Mathematics Subject Classification

Primary 42C05. Secondary 30C15, 40A30.

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