A new extension of Meixner-Pollaczek polynomials to d-orthogonality

W. Benamira, A. Nasri

The main object of this study is to introduce a new d-orthogonal polynomial set of Meixner-Pollaczek type, based on its hypergeometric representation. We derive various generating functions and provide explicit expressions for a connection formula and an inversion formula. Additionally, we investigate recurrence relations and explore the σ-Appell property. Furthermore, we establish a (d+1)-order recurrence relation and discuss representations of the dual sequence in terms of integrals involving the Meijer G-function. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(1) (2025), pp. 185-197