Author:
Brown Gavin,Wang Kun-Yang
Abstract
AbstractBest-possible results are established for positivity of the partial sums of Σ sin k θ (k + α)−1. In fact odd sums are positive for −1 ≤ α ≤ α0 = 2.1 …, while 2k terms are positive on the subinterval ]0, π − 2μ0π(4k +1)−1 [, μ0 = 0.8128 …. This is analagous to the Gasper extension of the Szegö-Rogosinski-Young inequality for cosine sums.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
Cited by
11 articles.
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1. Sharp inequalities for sine polynomials;Publicationes Mathematicae Debrecen;2022-01-01
2. On the scientific work of Kunyang Wang;International Journal of Wavelets, Multiresolution and Information Processing;2014-09
3. Preface;International Journal of Wavelets, Multiresolution and Information Processing;2014-09
4. Inequalities for Trigonometric Sums;Springer Optimization and Its Applications;2012
5. On the positivity of certain trigonometric sums and their applications;Computers & Mathematics with Applications;2011-11