A basic class of symmetric orthogonal polynomials using the extended Sturm-Liouville theorem for symmetric functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:325

Article

Masjed-Jamei, Mohammad

关键词: extended Sturm-Liouville theorem for symmetric functions;    orthogonal polynomials;    Favard's theorem;    Pearson distributions family;    dual symmetric distributions family;    generalized ultraspherical polynomials;    fifth and sixth kind of Chebyshev polynomials;    generalized Hermite polynomials;    two kinds of finite classical symmetric orthogonal polynomials;   

DOI  :  10.1016/j.jmaa.2006.02.007

来源: Elsevier

【 摘 要 】

In this research, by applying the extended Sturm-Liouville theorem for symmetric functions, a basic class of symmetric orthogonal polynomials (BCSOP) with four free parameters is introduced and all its standard properties, such as a generic second order differential equation along with its explicit polynomial solution, a generic orthogonality relation, a generic three term recurrence relation and so on, are presented. Then, it is shown that four main sequences of symmetric orthogonal polynomials can essentially be extracted from the introduced class. They are respectively the generalized ultraspherical polynomials, generalized Hermite polynomials and two other sequences of symmetric polynomials, which are finitely orthogonal on (-infinity, infinity) and can be expressed in terms of the mentioned class directly. In this way, two half-trigonometric sequences of orthogonal polynomials, as special sub-cases of BCSOP are also introduced. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free