Hypergeometric Orthogonal Polynomials with respect to Newtonian Bases - Vinet, L.; Zhedanov, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
We introduce the notion of ''hypergeometric'' polynomials with respect to Newtonian bases. We find the necessary and sufficient conditions for the polynomials Pn(x) to be orthogonal. For the special cases where the sets λn correspond to the classical grids, we find the complete solution to these conditions and observe that it leads to the most general Askey-Wilson polynomials and their special and degenerate classes.