## New bounds for the extreme zeros of Jacobi polynomials

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- by Geno Nikolov
- Proc. Amer. Math. Soc.
**147**(2019), 1541-1550 - DOI: https://doi.org/10.1090/proc/14370
- Published electronically: January 8, 2019
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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.## References

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## Bibliographic 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 1541-1550 - MSC (2010): Primary 33C45; Secondary 42C05
- DOI: https://doi.org/10.1090/proc/14370
- MathSciNet review: 3910419