I have to calculate the following quantity
where $\gamma(s,x)$ is the lower incomplete gamma function. Choosing the series representation I'm trying to actually sum the series, but I can't find a compact answer. Let $x=R/\alpha$
I was thinking in manipulations like multiplying the series by the factor of $x^2$ but the point will be in some convenient way of writing
to get the $1/n!$ for the exponential series. So far
but I can't give the number the way I want. Of course I'm assuming that what I want to do is possible, which may not be the case.
Thanks for your time.