Some Analytical Properties of the Hyperbolic Sine Integral

TL;DR

This paper investigates the mathematical properties of the hyperbolic sine integral, deriving inequalities and bounds that enhance understanding of its behavior and applications.

Contribution

It introduces new analytical properties and inequalities for the hyperbolic sine integral, including bounds for related functions like the hyperbolic tangent.

Findings

Established monotonicity of the hyperbolic sine integral

Derived inequalities involving the hyperbolic sine integral

Obtained rational bounds for the hyperbolic tangent function

Abstract

By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational bounds for the hyperbolic tangent function.