Inequalities of Fejér-Jackson Type
Date
2003Source
Monatshefte fur MathematikVolume
139Issue
2Pages
89-103Google Scholar check
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We complement, extend, and sharpen some known inequalities for sine sums. Our main result is the following refinement of the classical Fejér-Jackson inequality: For all integers n ≥ 2 and real numbers x ∈ (0, π) we have αx2(cotx/2-π-x/2) < ∑ k=1nsin(kx)/k with the best possible constant factor α = 1. This improves an inequality due to Turán.