Pré-Publication, Document De Travail Année : 2021

Tight exponential bounds for hyperbolic tangent

Résumé

We aim to obtain very tight exponential bounds for hyperbolic tangent by first establishing simple algebraic bounds for this function. Our inequalities refine a double inequality for tanh x recently proved by Zhang and Chen. In addition, a graphical analysis is carried out, and a number of auxiliary lemmas may be of use on their own.

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Dates et versions

hal-03167430 , version 1 (12-03-2021)

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  • HAL Id : hal-03167430 , version 1

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Yogesh J. Bagul, Ramkrishna M. Dhaigude, Christophe Chesneau, Marko Kostić. Tight exponential bounds for hyperbolic tangent. 2021. ⟨hal-03167430⟩
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