Third degree classical forms Original Research Article

Examples of semi-classical forms which are of third degree are not available in the literature. To enrich this new category of forms, our aim is to investigate all classical forms (semi-classical forms of class s=0) which are of third degree. In this paper, we find the conditions which should be fulfilled for a semi-classical form to be a third degree one. Using these results, we show that Hermite, Laguerre and Bessel forms are not third degree forms, only Jacobi forms satisfying some conditions which possess this property.