Affiliation:
1. Henan Polytechnic University, School of Mathematics and Informatics, China
2. University of Belgrade, School of Electrical Engineering, Serbia
Abstract
In this paper, we establish sharp inequalities for trigonometric functions. For example, we consider the Wilker inequality and prove that for 0 < x < ?/2 and n ? 1, 2 + (?n?1 j=2 dj+1x2j+ ?nx2n) x3 tan x < (sin x/x)2 + tan x/x < 2 + (?n?1 j=3 dj+1x2j+ Dnx2n) x3 tan x with the best possible constants ?n = dn and Dn = 2?6 ? 168?4 + 15120/945?4 (2/?) 2n ? ?n?1 j=2 dj+1 (2/?/)2n?2j , where dk = 22k+2 ((4k + 6) |B2k+2| + (?1)k+1)/(2k + 3)! and Bk are the Bernoulli numbers (k ? N0 := N? {0}). This improves and generalizes the results given by Mortici, Nenezic and Malesevic.
Funder
Ministry of Education, Science and Technological Development of the Republic of Serbia
Publisher
National Library of Serbia
Reference60 articles.
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