Sharp inequalities for trigonometric sums in two variables
Alzer, Horst ; Koumandos, Stamatis
Illinois J. Math., Tome 48 (2004) no. 3, p. 887-907 / Harvested from Project Euclid
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We prove several new inequalities for trigonometric sums in two variables. One of our results states that the double-inequality ¶ \begin{align} -\frac{2}{3}(\sqrt{2}-1) &\leq \sum_{k=1}^{n}\frac{\cos((k-1/2)x)\sin((k-1/2)y)}{k-1/2}\leq 2 \end{align} ¶ holds for all integers $n\geq 1$ and real numbers $x,y \in [0,\pi]$. Both bounds are best possible.
Publié le : 2004-07-15
Classification:  26D05,  41A17,  42A05 
@article{1258131058,
     author = {Alzer, Horst and Koumandos, Stamatis},
     title = {Sharp inequalities for trigonometric sums in two variables},
     journal = {Illinois J. Math.},
     volume = {48},
     number = {3},
     year = {2004},
     pages = { 887-907},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258131058}
}

Alzer, Horst; Koumandos, Stamatis. Sharp inequalities for trigonometric sums in two variables. Illinois J. Math., Tome 48 (2004) no. 3, pp.  887-907. http://gdmltest.u-ga.fr/item/1258131058/