Simple bounds for the extreme zeroes of Jacobi polynomials

2024/06/02 by Nikolov, Geno
#33C45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.00849

Abstract

Some new bounds for the extreme zeroes of Jacobi polynomials are obtained with an elementary approach. A feature of these bounds is their simple forms, which make them easy to work with. Despite their simplicity, our lower bounds for the largest zeroes of Gegenbauer polynomials are compatible with some of the best hitherto known results.

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