A GENERALIZATION OF JORDAN'S INEQUALITY AND AN APPLICATION

作者：Huo, Zhen-Hong; Niu, Da-Wei; Cao, Jian; Qi, Feng^*

来源：Hacettepe Journal of Mathematics and Statistics, 2011, 40(1): 53-61.

• Jordan's inequality
• Yang's inequality
• L'Hospital's rule
• Refinement
• Application

In this article, a new generalization of Jordan's inequality
Sigma(n)(k=1) mu(k) (theta(t) - x(t))(k) <= sin x/x - sin theta/theta <= Sigma(n)(k=1) omega(k) (theta(t) - x(t))(k)
for t >= 2, n is an element of N and theta is an element of (0,pi] is established, where the coefficients mu(k) and omega(k) are defined by recursion formulas, and are the best possible. As an application, Yang's inequality is refined.

• 出版日期2011-2
• 单位杭州师范大学; 天津工业大学; 中原工学院