Generalized Dunkl–Appell Polynomials

In this paper, we introduce a new d-orthogonal polynomial sequence by resolving a characterization problem involving a generalized Dunkl operator. We give some properties of this family, namely, a generating function, the fold symmetry property, a higher-order recurrence relation and differential–difference equation, the inversion formula, the explicit expression of the moments and their integral representations associated with the canonical d-dimensional functional vector ensuring the d-orthogonality as well as the components with respect to a cyclic group of finite order. We recover, as particular cases, some new and known results.