Classical orthogonal polynomials with respect to a lowering operator generalizing the Laguerre operator

Abstract

In this paper, we introduce the lowering operator Ωˆ1, c =Ωˆ1−cD 2, where c is an arbitrary complex number and Ωˆ1 is the generalized Laguerre operator introduced by Dattoli and Ricci. Then, we establish an intertwining relation between the operators Ωˆ1, c and the standard derivative D. On the other hand, an analogue of the Hahn characterization of D-classical orthogonal polynomials is given for the operator Ωˆ1, c . As a consequence, some integral relations between the corresponding polynomials are deduced. Finally, some expansions in series of Laguerre polynomials are studied.