Difference equations for a class of twice-iterated Hahn-Appell sequences of polynomials

Abstract

In this paper we consider a family of twice iterated Hahn-Appell polynomials (TI H-AP), which includes the twice iterated and the usual versions of Appell, ω-Appell and q-Appell polynomials. An equivalence theorem for the definition including the explicit representation and the generating function is given. Then determinantal representation, pure recurrence relation, lowering, rasing operators and difference equation by means of Hahn difference operator are obtained for these polynomials. As an application of the main results, we provide some results for 2-orthogonal Hahn-Appell polynomials in terms of one-orthogonal version. In the last section, we introduce the Hahn-Bernoulli, Hahn-Euler, HahnGenocchi and twice-iterated Hahn-Bernoulli-Euler polynomials