On generating symmetric orthogonal polynomials

Abstract

In this article, we show how to generate symmetric sequences of orthogonal polynomials whose moments are given. The advantage of this method is that only one Hankel determinant must be calculated. Three illustrative examples are presented in this sense.

Keywords:

• symmetric orthogonal polynomials
• Favard's theorem
• Hankel determinant
• three-term recurrence relation
• symmetric weight function

AMS Subject Classification:

• 33C45

Acknowledgments

This research was supported by a grant from “Bonyade Mellie Nokhbegan” No. PM/1184.