Tight Exponential Bounds For Hyperbolic Tangent - Yogesh J. Bagul; Ramkrishna M. Dhaigude; Christophe Chesneau; Marko Kostić (Jordan Journal of Mathematics and Statistics, 2025)
In this article, we aim to obtain very tight exponential bounds for the hyperbolic tangent function. Our inequalities refine a double inequality recently proved by Zhang and Chen. In addition, graphical and numerical analysis are carried out, and a number of auxiliary lemmas may be of use on their own. Key words and phrases. Hyperbolic tangent, sigmoidal function, hyperbolic cosine, exponential bounds. 2010 Mathematics Subject Classification. 26A09, 26D07, 33B10