Error function inequalities

• Authors: Horst Alzer
• Venue: Advances in Computational Mathematics
• Year: 2010

We present various inequalities for the error function. One of our theorems states: Let 驴驴驴驴1. For all x,y驴驴0 we have $$ \delta_{\alpha} with the best possible bounds $$ \delta_{\alpha}= \left\{ \begin{array}{ll} 1+\sqrt{\pi}/2, & \ \ \textrm{{if} $\alpha=1$,}\\ \sqrt{\pi}/2, & \ \ \textrm{{if} $\alpha1$,}\\ \end{array}\right. \quad{\mbox{and} \,\,\,\,\, \Delta_{\alpha}=1+\frac{1}{\mbox{erf}(1)}.} $$