A Sharp Inequality for a Trigonometric Sum
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- 作者：Horst Alzer (1)
Stamatis Koumandos (2) - 关键词：Primary 42A05 ; Secondary 26D05 ; Inequalities ; sine sums ; cosine sums
- 刊名：Mediterranean Journal of Mathematics
- 出版年：2013
- 出版时间：February 2013
- 年：2013
- 卷：10
- 期：1
- 页码：313-320
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Stamatis Koumandos (2)
1. Morsbacher Str. 10, D-51545, Waldbr枚l, Germany
2. Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus - ISSN：1660-5454
文摘
We prove that the inequality $$-\frac{1}{2}\leq {\sum\limits_{k=1}^{n}} \left( \frac{{\rm cos}(2kx)}{2k - 1}+\frac{{\rm sin}((2k - 1)x)}{2k} \right)$$ holds for all natural numbers n and real numbers x with ${x \in [0, \pi]}$ . The sign of equality is valid if and only if n =聽 1 and x =聽 蟺 /2.