New inequalities between the inverse hyperbolic tangent and the analogue for corresponding functions

Abstract

Abstract In this paper, we present new inequalities which reveal further relationship for both the inverse tangent function arctan ( x ) $\arctan (x)$ and the inverse hyperbolic function arctanh ( x ) $\operatorname{arctanh}(x)$ . At the same time, we give the analogue for inverse hyperbolic tangent and other corresponding functions.

Keywords

• Inequalities
• Inverse tangent function
• Inverse hyperbolic sine function
• Inverse hyperbolic tangent function
• Inverse sine function