Quasi-orthogonality and zeros of some [formula omitted] and [formula omitted] polynomials

Abstract

We state and prove the q-extension of a result due to Johnston and Jordaan (cf. Johnston and Jordaan (2015)) and make use of this result, the orthogonality of q-Laguerre, little q-Jacobi, q-Meixner and Al-Salam–Carlitz I polynomials as well as contiguous relations satisfied by the polynomials, to establish the quasi-orthogonality of certain 2ϕ2 and 3ϕ2 polynomials. The location and interlacing properties of the real zeros of these quasi-orthogonal polynomials are studied. Interlacing properties of the zeros of q-Laguerre quasi-orthogonal polynomials Ln(δ)(z;q) when −2<δ<−1 with those of Ln−1(δ+1)(z;q) and Ln(δ+1)(z;q) are also considered.