SOME SHARP CIRCULAR AND HYPERBOLIC BOUNDS OF exp(−x²) WITH APPLICATIONS

This article is devoted to the determination of sharp lower and upper bounds for exp(−x²) over the interval (−∈, ∈). The bounds are of the type [ a + f ( x ) a + 1 ] α , where f(x) denotes either cosine or hyperbolic cosine. The results are then used to obtain and rene some known Cusa-Huygens type i...

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Bibliographic Details
Published in:Applicable analysis and discrete mathematics 2020-04, Vol.14 (1), p.239-254
Main Authors: Bagul, Yogesh J., Chesneau, Christophe
Format: Article
Language:English
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Summary:This article is devoted to the determination of sharp lower and upper bounds for exp(−x²) over the interval (−∈, ∈). The bounds are of the type [ a + f ( x ) a + 1 ] α , where f(x) denotes either cosine or hyperbolic cosine. The results are then used to obtain and rene some known Cusa-Huygens type inequalities. In particular, a new simple proof of Cusa-Huygens type inequalities is presented as an application. For other interesting applications of the main results, sharp bounds of the truncated Gaussian sine integral and error functions are established. They can be useful in probability theory.
ISSN:1452-8630
2406-100X
DOI:10.2298/AADM190123010B