Sophomore's dream function: asymptotics, complex plane behavior and relation to the error function

V. Yu. Irkhin

Sophomore's dream sum $S={\sum }_{n=1}^{\infty }{n}^{-n}$ is extended to the function $f(t,a)=t{\int }_0^1(ax{)}^{-tx}dx$ with $f(1,1)=S$. Asymptotic behavior for a large $|t|$ is obtained…