Tight Exponential Bounds For Hyperbolic Tangent
Keywords:
Hyperbolic tangent, sigmoidal function, hyperbolic cosine, exponential bounds.Abstract
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
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Published
2025-05-18
How to Cite
Yogesh J. Bagul, Ramkrishna M. Dhaigude, Christophe Chesneau, & Marko Kostić. (2025). Tight Exponential Bounds For Hyperbolic Tangent. Jordan Journal of Mathematics and Statistics, 15(4A), 807–821. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/699
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