The Strong Chebyshev Distribution and Orthogonal Laurent Polynomials

✍ Scribed by S.Clement Cooper; Philip E Gustafson

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 264 KB
• Volume: 92
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1997.3161

✦ Synopsis

The strong Chebyshev distribution and the Chebyshev orthogonal Laurent polynomials are examined in detail. Explicit formulas are derived for the orthogonal Laurent polynomials, uniform convergence of the associated continued fraction is established, and the zeros of the Chebyshev L-polynomials are given. This provides another well-developed example of a sequence of orthogonal L-polynomials. 1998 Academic Press 1. INTRODUCTION In 1980, the paper entiled ``A Strong Stieltjes Moment Problem'' by William B. Jones, W. J. Thron, and Haakon Waadeland appeared and opened up the study of strong distributions and orthogonal Laurent polynomials. Several examples of orthogonal Laurent polynomial are in the literature including [4 6, 9 11, 20]. In [21], several strong distributions were introduced and here we closely examine the strong Chebyshev distribution which first appeared there. Our reasons for developing this example are two-fold. The first is that examples often provide insight that suggests further lines of study. Second, the classical Chebyshev polynomials Article No. AT973161 361