ok, I expanded just the exp, and now I've this, (with some transformations) and quite looks like what I want.
\sum_1^\infty \frac{1}{n!}\int_0^\infty e^{-y(n+1)}y^n
but now?
but I've to pass through the euler's gamma representation, and expanding this function is quite horrible using taylor. I'll try anyway with your idea!,Ty!
Homework Statement
Using Euler's Gamma and a proper substitution prove the relation above:
\int_0^1 1/x^x=\sum_{n=1}^\infty 1/n^n
Homework Equations
How to resolve this XD?
The Attempt at a Solution