Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences

Stieltjes interlacing states that if {pn(z)}n=0∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{p_{n}(z)\}_{n=0}^{\infty }$\end{document} is a sequence of orthogonal polynomials, then there is at least one zero of pn(z) in between any two consecutive zeros of pm(z), where m < n − 1. Stieltjes interlacing holds for the zeros of polynomials from different sequences of little q-Jacobi polynomials pn(z;a,b|q), 0 < aq < 1, bq < 1 and q-Laguerre polynomials Ln(δ)(z;q),δ>−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L_{n}^{(\delta )}(z;q),\delta >-1$\end{document}. We consider cases where the degree difference is 2 or 3 and, in each case, we derive the associated polynomials analogous to the de Boor-Saff polynomials whose zeros will complete the interlacing. We derive upper bounds for the smallest zeros of these polynomials and provide numerical examples to illustrate improvements on previously known bounds that have been obtained using different approaches.