Second degree semi-classical forms of class s=1. The symmetric case

✍ Scribed by Driss Beghdadi

• Book ID: 104308666
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 102 KB
• Volume: 34
• Category: Article
• ISSN: 0168-9274
• DOI: 10.1016/s0168-9274(99)00032-x

✦ Synopsis

A form (linear functional) u is called regular if there exists a sequence of polynomials {P n } n 0 , deg P n = n, which is orthogonal with respect to u. Such a form is said to be semi-classical, if there exist two polynomials Φ and Ψ such that (Φu) + Ψ u = 0. Now, this form is said to be of second degree if its formal Stieltjes function (see (1.1)) satisfies a second degree equation.

Recently, all the second degree classical forms (semi-classical forms of class s = 0) are determined. In this paper, we determine all the symmetric semi-classical forms of class s = 1, which are also of second degree. Only some forms, introduced by Chihara, which satisfy a certain condition, possess this property. We show that there exists a relation between these forms and the second degree classical ones.