Inundated with Greek letters

 The Poisson distribution has Euler's number in it, its doing symbolic multiply. That should be a 16th order polynomial, and lamba should be a rational fraction. It causes problems when do the probability of L1-L2, the difference of two queues, one in and one out. That distribution likely is polynomial, but I have done no work on it. Anyway, the Newtons version of that distribution is this:

This is one of those spots where some theory seems to be missing. This distribution on the left has a Bessel function, the integral of a sine and other stuff.  But it should all come down to a power series, or a power series of a compact polynomial.

Makes me a bit stuck, and seeing as how lazy I am; being stuck is compound.  This is where professional mathematicians get huge quantities and rewards.