Hahn-Appell polynomials and their d-orthogonality

Abstract

Recently, parametric (q,)-exponential functions were defined in [4]. In the present paper, we obtain non-parametric Hahn exponential functions by using the characteristic properties of the usual discrete and q-exponential functions. We introduce Hahn-Appell polynomials and prove that their generating function is written by means of this new non-parametric exponential function. We further obtain a recurrence relation, difference equation and determinantal representation of Hahn-Appell polynomials. Finally, we determine the generating function of the Hahn-Appell polynomials which are also d-orthogonal and obtain the form of d-dimensional functional vector which ensures the d- orthogonality.