Sharp inequalities for trigonometric sums in two variables
SourceIllinois Journal of Mathematics
Google Scholar check
MetadataShow full item record
We prove several new inequalities for trigonometric sums in two variables. One of our results states that the double-inequality -2/3(√2 - 1) ≤ Σk=1n cos((k - 1/2)x) Sin((k - 1/2)y)/k - 1/2 ≤ 2 holds for all integers n ≥ 1 and real numbers x, y ε [0, π]. Both bounds are best possible. ©2004 University of Illinois.