Mixed recurrence relations and interlacing of the zeros of some q-orthogonal polynomials from different sequences

被引：0
|
作者：
K. Jordaan
F. Toókos
机构：
[1] University of Pretoria,Department of Mathematics and Applied Mathematics
[2] Institute for Biomathematics and Biometry,undefined
[3] Helmholtz Zentrum München,undefined
来源：
Acta Mathematica Hungarica | 2010年 / 128卷
关键词：
-orthogonal polynomial; zero; interlacing of zeros; separation of zeros; polynomial; Al-Salam-Chihara; continuous ; -ultraspherical; -Meixner-Pollaczek; -Laguerre; 30C15; 33D45; 42C05;
D O I：
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学科分类号：
摘要：
We use the generating functions of some q-orthogonal polynomials to obtain mixed recurrence relations involving polynomials with shifted parameter values. These relations are used to prove interlacing results for the zeros of Al-Salam-Chihara, continuous q-ultraspherical, q-Meixner-Pollaczek and q-Laguerre polynomials of the same or adjacent degree as one of the parameters is shifted by integer values or continuously within a certain range. Numerical examples are given to illustrate situations where the zeros do not interlace.
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页码：150 / 164
页数：14
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