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Sharp inequalities on circular and hyperbolic functions using Bernoulli inequality types

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In using variants of the so-called Bernoulli inequality, new sharp bounds for circular and hyperbolic functions are proved as well as for their products and ratios. We provide some improvements of previous results by using infinite products and power series expansions.

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Acknowledgements

I would like to thank the referees for valuable comments and suggestions.

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  1. University of Paris, 4, Cour des Quesblais, Saint-Pere, 35430, Paris, France

    Abd Raouf Chouikha

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  1. Abd Raouf Chouikha
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Chouikha, A.R. Sharp inequalities on circular and hyperbolic functions using Bernoulli inequality types. RACSAM 115, 143 (2021). https://doi.org/10.1007/s13398-021-01086-4

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  • DOI: https://doi.org/10.1007/s13398-021-01086-4

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