Sharp inequalities for trigonometric sums in two variables
Date
2004Source
Illinois Journal of MathematicsVolume
48Issue
3Pages
887-907Google Scholar check
Metadata
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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.