On the moments of Laguerre-Hahn linear forms of class zero

Abstract

The purpose of this paper is to provide a constructive method for generating the moments of Laguerre-Hahn linear forms of class zero. The approach relies on a general algebraic system on the moments, equivalent to the Laguerre-Hahn functional equation for forms of arbitrary class, from which the restriction to class zero yields explicit recurrences allowing the entire moment sequence to be built recursively from the first moment. These recurrences are applied to each of the ten canonical class-zero families, and the corresponding first moments are derived explicitly via a {\it Mathematica$^{\circledR}$} implementation.