TITLE: What's the sum of $\sum \limits_{k=1}^{\infty}\frac{t^{k}}{k^{k}}$?
QUESTION [5 upvotes]: Absolute convergence and uniform convergence are easy to determine for this power series. However, it is nontrivial to calculate the sum of $\large\sum \limits_{k=1}^{\infty}\frac{t^{k}}{k^{k}}$.

REPLY [6 votes]: I asked a similar question here. That question led Owen and me to the function you asked and we wrote up some nice (an incomplete version) properties here. To give a short answer to your question, $$\sum_{k=1}^{\infty} \frac{t^k}{k^k} = t \int_0^{1} x^{-tx}dx$$