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A pair of optimal inequalities related to the error function
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
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