In this paper, we prove the quasi-orthogonality of a family of 2F2 polynomials and several classes of 3F2 polynomials that do not appear in the Askey scheme for hypergeometric orthogonal polynomials. Our results include, as a special case, two 3F2 polynomials considered by Dickinson in 1961. We also discuss the location and interlacing of the real zeros of our polynomials.
The family of general Jacobi polynomials P(α,β)
n where α, β ∈ C can be characterised by complex (non-
Hermitian) orthogonality relations (cf. Kuijlaars et al. (2005)). The special subclass of Jacobi polynomials