Some Sharp Circular and Hyperbolic Bounds of exp(-x^2 ) with Applications

Applicable Analysis and Discrete Mathematics

article

Yogesh J. Bagul¹  Christophe Chesneau² 

[1] Department of Mathematics, K. K. M. College;LMNO, University of Caen Normandie

关键词: Cusa-Huygens inequality;    Truncated Gaussian sine integral;    Exponential;    Cicular;    hyperbolic;   

DOI  :  10.2298/AADM190123010B

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Bounds of the exponential function exp(−x2) can be useful in many areasof mathematics where it appears, mainly to evaluate analytically or numericallycomplex integrals involving it. Recent studies show that there is still a room ofimprovements; sharp and tractable bounds for this function remain an actual challenge for any contemporary mathematician. In this regard, Chesneau [8, 9] gavetight lower bounds of exp(x2) over the real line. For some other sharp bounds,see [3, 4], where the bounds are obtained over (0, 1) by the use of circular andhyperbolic functions. This type of bounds can in fact be obtained naturally over(0, π/2)(see [10]). Interested readers are referred to [2, 8, 9, 14, 20], and thereferences therein.

【 授权许可】

Unknown