On the cubic decomposition of a family ofGq-semiclassical polynomial sequences of class one

In the present work, we deal with a monic orthogonal polynomial sequence (MOPS) inferred by its cubic decomposition W3n(x)=Pn(x3). Our aim is to describe all Hq-semiclassical q-polynomials of class one of these sequences. From the cubic decomposition structure and via the study of the q-difference equation satisfied by its corresponding regular form w where Hq is the Hahn’s operator, only three MOPSs appear and their recurrence coefficients are explicitly given. A discrete measure representation of each corresponding linear functional is also established.