This is a curiosity question.
Let's consider the following sum: $$S=\sum_{n=0}^{+\infty} \frac{1}{\sqrt{ n !}}$$
The question asked to prove its convergence, which I did using the ratio test. So I tried to find a closed form for the this sum but without luck.
My question
1) Is there a closed form for $S$? (very likely no). 2) If the answer is no can we prove that there is no closed form for $S$ rigorously?
Thanks,