\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} The equation below is sometimes
attributed to Atle Selberg, a prominent and long-lived Norwegian
mathematician (1907--2007) with the remark that he discovered it while
a teenager. This is a nice legend, but the problem apparently also
appears in an English calculus book of the 1920's and perhaps
before. So: verify that

$$\int_0^1 x^{-x} dx = \sum_{n=1}^{\infty} {1 \over {n^n}}.$$

\noindent {\bf Hint} Get a reduction formula for $\int x^n(\ln
x)^m\,dx$, and use it improperly. The value of both sides of the
equation is approximately 1.291285997. I don't know any use for
this formula besides its lovely existence.

\vfil\eject\end