m-Symmetric Generalized Hypergeometric d-Orthogonal Polynomials

Abstract

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 class  D, m< d. The solution provides new d-orthogonal polynomial sequences to be classified in the d-Askey-scheme and also has an m-symmetry property with m<d. This class contains the Gould-Hopper polynomial sequence,   the class considered by Ben Cheikh-Douak.  This class contains new d-orthogonal polynomial sequences not belonging to class  A. 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.