I was wondering if we have a formula for the following function:
$$ f(x) = \frac{1}{x^{0!}} + \frac{1}{x^{1!}} + \frac{1}{x^{2!}} + \frac{1}{x^{3!}} + ... = \sum_{n=0}^{\infty}x^{-n!} $$
(Like we have for the geometric series):
$$ \sum_{k=0}^{\infty}x^{-k} =\frac{1}{1-x} $$
Or even if we have nice values for similar functions (infinite sums that has factorials in the exponents) or if we can evaluete any value of f(x) like: $$f(e),f(2)...$$