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Title: Rogosinski-Szegö type inequalities for trigonometric sums
Authors: Alzer, H
Kwong, MK
Keywords: Inequalities
Sharp bounds
Trigonometric sums
Issue Date: 2015
Publisher: Academic Press Inc.
Source: Journal of approximation theory, 2015, v. 190, p. 62-72 How to cite?
Journal: Journal of Approximation Theory 
Abstract: We prove that the inequalities ∑k=1nsin(kx)k+1≥1384(9-137)110-6137=-0.044419686... and ∑k=1nsin(kx)+cos(kx)k+1≥-12 are valid for all real numbers x∈. [0, π] and all positive integers n. The constant lower bounds are sharp. Our theorems complement a classical result of Rogosinski and Szegö, who proved in 1928 that the inequality ∑k=1ncos(kx)k+1≥-12 holds for all x∈. [0, π] and n≥. 1.
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.04.007
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