#2, October 2002




Let $A_n$ for $n\ge 1$ be constants such that

\begin{displaymath} \int_{-\infty}^{\infty}{ \frac{A_n}{(x^2+1)^{n+1/2}} dx } = 1. \end{displaymath}

Show that for some constant C, the following inequality holds:

\begin{displaymath} A_n \le \sqrt{n} \end{displaymath}

(the smallest constant C wins).