Sharp upper and lower bounds for a sine polynomial

被引：6
|
作者：
Alzer, Horst [1 ]
Kwong, Man Kam [1 ]
机构：
[1] Hong Kong Polytech Univ, Dept Appl Math, Hunghom, Hong Kong, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 275卷
关键词：
Fejer-Jackson inequality; Sine polynomial; Sharp bounds;
D O I：
10.1016/j.amc.2015.11.032
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that for all n >= 1 and x is an element of (0, pi) we have alpha <= Sigma(n)(k=1) sin(kx)/k(n + 1 - k) <= beta with the best possible constant bounds alpha = 3 - root 33/64 root 30 - 2 root 33 = -0.18450... and beta = 1. (C) 2015 Elsevier Inc. All rights reserved.
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页码：81 / 85
页数：5
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