Interlacing Properties and Bounds for Zeros of Some Quasi-Orthogonal Laguerre Polynomials

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• 作者：Kathy Driver ; Martin E. Muldoon
• 关键词：Interlacing of zeros ; Stieltjes-Theorem ; Laguerre polynomials ; Quasi ; orthogonal polynomials ; Primary 33C45 ; Secondary 26C10
• 刊名：Computational Methods and Function Theory
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：15
• 期：4
• 页码：645-654
• 全文大小：480 KB
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• 作者单位：Kathy Driver (1)
  Martin E. Muldoon (2)
  
  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, Rondebosch, 7701, South Africa
  2. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada
  
• 刊物主题：Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable;
• 出版者：Springer Berlin Heidelberg
• ISSN：2195-3724

文摘

We discuss interlacing properties of zeros of Laguerre polynomials of different degree in quasi-orthogonal sequences \(\{L_{n}^{(\alpha )}\} _{n=0}^\infty \) characterized by \(-2<\alpha <-1\). Interlacing of zeros of \(L_{n}^{(\alpha )},\) \(-2<\alpha <-1\), with zeros of orthogonal Laguerre polynomials is also investigated. Upper and lower bounds for the negative zero of \(L_{n}^{(\alpha )},\) \(-2<\alpha < -1,\) are derived. Keywords Interlacing of zeros Stieltjes-Theorem Laguerre polynomials Quasi-orthogonal polynomials