On some m-Symmetric Generalized Hypergeometric d-Orthogonal Polynomials

Journal Article

2023

Published in: https://doi.org/10.2298/FIL2404279B

Filomat

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 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.

• Volume Number: 24
• Issue Number: 4