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New bounds for the extreme zeros of Jacobi polynomials


Author: Geno Nikolov
Journal: Proc. Amer. Math. Soc. 147 (2019), 1541-1550
MSC (2010): Primary 33C45; Secondary 42C05
DOI: https://doi.org/10.1090/proc/14370
Published electronically: January 8, 2019
MathSciNet review: 3910419
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Abstract: We apply the Euler–Rayleigh method to the Jacobi and, in particular, the Gegenbauer polynomials, represented as hypergeometric functions, to prove new bounds for the extreme zeroes of these polynomials. Our bounds are shown to either reproduce or improve some of the recent results obtained by other authors.


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Additional Information

Geno Nikolov
Affiliation: Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria
MR Author ID: 131505
ORCID: 0000-0001-5608-2488
Email: geno@fmi.uni-sofia.bg

Received by editor(s): July 6, 2018
Published electronically: January 8, 2019
Additional Notes: This research was supported by the Bulgarian National Research Fund through Contract DN 02/14 and by the Sofia University Research Fund through Contract 80-10-139.
Communicated by: Mourad Ismail
Article copyright: © Copyright 2019 American Mathematical Society