A pair of optimal inequalities related to the error function
Functional Analysis
2009-09-25 v1
Abstract
The Error Function \begin{eqnarray} V(x) & \equiv & \sqrt{\pi} e^{x^2} [1 - \hbox{erf}(x)] \\ & = & \int_0^\infty \frac{ e^{-u} }{\sqrt{x^2 + u}} du = 2 e^{x^2}\int_x^\infty e^{-t^2} dt \nonumber \end{eqnarray} arises in many contexts, from probability to mathematical physics. We give estimates for the Error Function from above and below which are optimal within a certain class of functions.
Cite
@article{arxiv.math/9711207,
title = {A pair of optimal inequalities related to the error function},
author = {M. Beth Ruskai and Elisabeth Werner},
journal= {arXiv preprint arXiv:math/9711207},
year = {2009}
}