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New inequalities from classical Sturm theorems

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)

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. (Contact us about this Publication)
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
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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 20 Nov 2018 18:42 UTC
Last Modified: 05 Jun 2019 14:30 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70221 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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