Sharp inequalities for tangent function with applications - Hui-Lin Lv; Zhen-Hang Yang; Tian-Qi Luo; Shen-Zhou Zheng (Journal of Inequalities and Applications, 2017)
Abstract In the article, we present new bounds for the function e t cot ( t ) − 1 $e^{t\cot(t)-1}$ on the interval ( 0 , π / 2 ) $(0, π/2)$ and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the quotient of power series, which refine the Redheffer and Becker-Stark type inequalities for tangent function.