Hahn-Appell polynomials and their \(d\)-orthogonality (Q2317557)

In this paper, the authors introduce Hahn-Appell polynomial sequences by the following property \[ D_{q,\omega} P_n(x)=[n] P_{n-1}(x), \qquad n\geq 1, \] where \(D_{q,\omega}\) is the Hahn \((q,\omega)\) -difference operator and \([n]=\frac{1-q^n}{1-q}\). Then, the authors obtain generating function, recurrence relation, difference equation and determinantal representation for such polynomials.