Sharper bounds and new proofs of the exponential function with cotangent

Abstract

This paper provides a Páde interpolation based method for finding improved bounds for the exponential function with cotangent. In principle, it can recover many results in prevailing methods. A new method for proving the corresponding bounds is also proposed, which can also be applied for proving more other bounding functions. Numerical experiments show that the new bounds are better than those of prevailing methods.

Keywords

• bounds
• inequalities
• circular functions
• páde interpolation
• cotangent function