Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 1, 2013
Harmonic analysis
|
|
---|---|---|
Page(s) | 48 - 59 | |
DOI | https://doi.org/10.1051/mmnp/20138103 | |
Published online | 28 January 2013 |
Inequalities for Extreme Zeros of Some Classical Orthogonal and q-orthogonal Polynomials
1 Department of Mathematics and Applied
Mathematics, University of
Cape Town
7701,
RSA
2 Department of Mathematics and Applied
Mathematics, University of Pretoria, Pretoria, 0002, RSA
∗ Corresponding author. E-mail: kathy.driver@uct.ac.za
Let {pn}∞n=0 be a sequence of orthogonal polynomials. We briefly review properties of pn that have been used to derive upper and lower bounds for the largest and smallest zero of pn. Bounds for the extreme zeros of Laguerre, Jacobi and Gegenbauer polynomials that have been obtained using different approaches are numerically compared and new bounds for extreme zeros of q-Laguerre and little q-Jacobi polynomials are proved.
Mathematics Subject Classification: 33C45 / 42C05
Key words: Bounds for extreme zeros of orthogonal and q-orthogonal polynomials / common zeros of orthogonal polynomials / monotonicity / convexity / interlacing of zeros / separation of zeros / inequalities for zeros
© EDP Sciences, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.