LAUSR

In [9] I. Lamiri and M. Ouni state some characterization theorems for d-orthogonal polynomials of Hermite, Gould-Hopper and Charlier type polynomials. In [3] Y. Ben Cheikh I. Lamiri and M.Ouni give a characterization theorem for some classes of generalized hypergeometric polynomials containing for example, Gegenbauer polynomials, Gould-Hopper polynomials, Humbert polynomials, a generalization of Laguerre polynomials and a generalization of Charlier polynomials. In this work, we introduce a new class D of generalized hypergeometric m-symmetric polynomial sequence containing the Hermite polynomial sequence and Laguerre polynomial sequence. Then we consider a characterization problem consisting in finding the d-orthogonal polynomial sequences in the class D, m ? d. The solution provides new d-orthogonal polynomial sequences to be classified in d-Askey-scheme and also having a m-symmetry property with m ? d. This class contains the Gould-Hopper polynomial sequence, the class considered by Ben Cheikh-Douak, the class considered in [3]. This class contains new d-orthogonal polynomial sequences not belonging to the classA. We derive also in this work the d-dimensional functional vectors ensuring the d-orthogonality of these polynomials. We also give an explicit expression of the d-dimensional functional vector.