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

被引：0
作者：
Pinaki Prasad Kar
Kerstin Jordaan
Priyabrat Gochhayat
机构：
[1] Sambalpur University,Department of Mathematics
[2] University of South Africa,Department of Decision Sciences
来源：
Numerical Algorithms | 2023年 / 92卷
关键词：
Interlacing of zeros; Stieltjes interlacing; Bounds; Little ; -Jacobi polynomials; -Laguerre polynomials; 33D15; 33D45;
D O I：
暂无
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学科分类号：
摘要：
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.
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页码：723 / 746
页数：23
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