Deaño, Alfredo, Segura, Javier (2004) New inequalities from classical Sturm theorems. Journal of Approximation Theory, 131 (2). pp. 208-230. ISSN 0021-9045. (doi:10.1016/j.jat.2004.09.006) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:70221)
The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |
Official URL: https://doi.org/10.1016/j.jat.2004.09.006 |
Abstract
Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szeg?'s bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with , bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions
Item Type: | Article |
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DOI/Identification number: | 10.1016/j.jat.2004.09.006 |
Uncontrolled keywords: | Sturm comparison theoremHypergeometric functionsOrthogonal polynomials |
Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis Q Science > QA Mathematics (inc Computing science) > QA351 Special functions |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Alfredo Deano Cabrera |
Date Deposited: | 20 Nov 2018 18:42 UTC |
Last Modified: | 16 Nov 2021 10:25 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/70221 (The current URI for this page, for reference purposes) |
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