Other family of cubic decomposition of a semiclassical form of class one

Abstract

In the present work, we are interested in the study of a family of monic orthogonal polynomial sequence deduced by its cubic decomposition (CD) , . Our objective is to give some algebraic properties on its connecting sequences derived by the CD and essentially to deal with semiclassical character of this family of sequences. From the CD structure, only five semiclassical MOPS of class one appear, which their recurrence coefficients are explicitly given. An integral representation of positive definite case is established.