Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions

Abstract The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on exp(−x²), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbo...

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Autores principales:	Bagul,Yogesh J., Chesneau,Christophe
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2019
Materias:	Exponential function trigonometric function hyperbolic function
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000100021
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spelling	oai:scielo:S0719-064620190001000212019-08-09Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic FunctionsBagul,Yogesh J.Chesneau,Christophe Exponential function trigonometric function hyperbolic function Abstract The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on exp(−x²), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbolic cosine are very sharp. New proofs, refinements as well as new results are offered. Some graphical and numerical results illustrate the findings.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.21 n.1 20192019-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000100021en10.4067/S0719-06462019000100021
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Exponential function trigonometric function hyperbolic function
spellingShingle	Exponential function trigonometric function hyperbolic function Bagul,Yogesh J. Chesneau,Christophe Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions
description	Abstract The prime goal of this paper is to establish sharp lower and upper bounds for useful functions such as the exponential functions, with a focus on exp(−x²), the trigonometric functions (cosine and sine) and the hyperbolic functions (cosine and sine). The bounds obtained for hyperbolic cosine are very sharp. New proofs, refinements as well as new results are offered. Some graphical and numerical results illustrate the findings.
author	Bagul,Yogesh J. Chesneau,Christophe
author_facet	Bagul,Yogesh J. Chesneau,Christophe
author_sort	Bagul,Yogesh J.
title	Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions
title_short	Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions
title_full	Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions
title_fullStr	Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions
title_full_unstemmed	Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions
title_sort	some new simple inequalities involving exponential, trigonometric and hyperbolic functions
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462019000100021
work_keys_str_mv	AT bagulyogeshj somenewsimpleinequalitiesinvolvingexponentialtrigonometricandhyperbolicfunctions AT chesneauchristophe somenewsimpleinequalitiesinvolvingexponentialtrigonometricandhyperbolicfunctions
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Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions

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