Sharp inequalities for tangent function with applications

Abstract

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 ) $(0, \pi/2)$ 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.

Keywords

• trigonometric function
• inequalities
• Sine integral
• Catalan constant