What is the closed form for $\sum_{n=0}^{\infty}\frac{1}{(n!)^2}$? And is there a closed form for $\displaystyle \sum_{n=0}^{\infty}\frac{1}{(n!)^k}$?
Edit: If there are no closed forms for the two series, how should I convert them into integrals? Now I know that $\displaystyle I_0(2)=\sum_{n=0}^{\infty}\frac{1}{(n!)^2} = \frac{1}{\pi}\int_{0}^{\pi}e^{2\cos\theta}d\theta$, but is there an integral representation for $\displaystyle \sum_{n=0}^{\infty}\frac{1}{(n!)^k}$?