A Sharp Double Inequality for the Inverse Tangent Function

Authors

G. Alirezaei,

Abstract

        The inverse tangent function can be bounded by different inequalities, for example by Shafer’s inequality. In this paper, we propose a new sharp double inequality for the inverse tangent function. In particular, we sharpen Shafer’s inequality and calculate the best corresponding constants. The maximum relative errors of the obtained bounds are approximately smaller than 0.27% and 0.23% for the lower and upper bound, respectively. Furthermore, we determine an upper bound on the relative errors of the proposed bounds in order to describe their tightness analytically.

Submitted

to MIA on Monday, 15. July 2013.

BibTEX Reference Entry 

@article{Al11,
	author = {Gholamreza Alirezaei},
	title = "A Sharp Double Inequality for the Inverse Tangent Function",
	journal = "Mathematical Inequalities {\&} Applications",
	year =  -11,
	}

Downloads

 Download paper  Download bibtex-file

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights there in are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.