A Sharp Inequality for a Trigonometric Sum

被引：0

作者：

Alzer, Horst ^{[1
]}

Koumandos, Stamatis ^{[1
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2013年 / 10卷 / 01期

关键词：

Inequalities; sine sums; cosine sums; 2; VARIABLES; POLYNOMIALS; SERIES; FOURIER;

D O I：

10.1007/s00009-012-0188-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the inequality -1/2 <= Sigma(n)(k=1) (COS(2kx)/2k - 1) + sin((2k - 1)x)/2k) holds for all natural numbers n and real numbers x with x epsilon [0, pi]. The sign of equality is valid if and only if n = 1 and x = pi/2.

引用

页码：313 / 320

页数：8

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