Inequalities of Fejér-Jackson Type
SourceMonatshefte fur Mathematik
Google Scholar check
MetadataShow full item record
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.