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

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 $\sigma $-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.