ScholarLens Back to search
2021•jnanabhaOpen access

ON SIMPLE BOUNDS FOR INVERSE HYPERBOLIC SINE AND INVERSE HYPERBOLIC TANGENT FUNCTIONS

Ramkrishna M. Dhaigude, Sumedh B. Thool, Yogesh J. Bagul, Vinay M. Raut

Open full text 2 citations

Abstract

We obtain simple algebraic bounds of inverse hyperbolic sine and inverse hyperbolic tangent functions i.e., sinh⁻¹ x and tanh⁻¹ x. The inequalities are obtained on the entire domains of these functions. From our results, we obtain tighter bounds for the same functions. The Wilker and Huygens type inequalities involving inverse hyperbolic functions can also be easily derived from our main results.

Open-access reader

About this research paper

What this paper is about

We obtain simple algebraic bounds of inverse hyperbolic sine and inverse hyperbolic tangent functions i.e., sinh⁻¹ x and tanh⁻¹ x. The inequalities are obtained on the entire domains of these functions. From our results, we obtain tighter bounds for the same functions. The Wilker and Huygens type inequalities involving inverse hyperbolic functions can also be easily derived from our main results.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We obtain simple algebraic bounds of inverse hyperbolic sine and inverse hyperbolic tangent functions i.e., sinh⁻¹ x and tanh⁻¹ x. The inequalities are obtained on the entire domains of these functions. From our results, we obtain tighter bounds for the same functions. The Wilker and Huygens type inequalities involving inverse hyperbolic functions can also be easily derived from our main results.

Key concepts: Hyperbolic function, Inverse hyperbolic function, Inverse trigonometric functions, Mathematics, Inverse, Simple (philosophy), Sine, Inverse function

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
ON SIMPLE BOUNDS FOR INVERSE HYPERBOLIC SINE AND INVERSE HYPERBOLIC TANGENT FUNCTIONS — Research Paper | ScholarLens