Quasi-orthogonality and real zeros of some F22 and F23 polynomials

In this paper, we prove the quasi-orthogonality of a family of F22 polynomials and several classes of F23 polynomials that do not appear in the Askey scheme for hypergeometric orthogonal polynomials. Our results include, as a special case, two F23 polynomials considered by Dickinson in 1961. We also discuss the location and interlacing of the real zeros of our polynomials.