Summation with Factorial

1. Nov 27, 2012

Polymath89

I need to simplify this expression and I don't know how to deal with the factorials in the sum

$$e^{-(\lambda + \mu)}\sum_{k=0}^w \frac{\lambda^k \mu^{(w-k)}}{k!(w-k)!}$$

Can anybody give me a hint on how to sum over the factorials?

2. Nov 27, 2012

Staff: Mentor

This is already pretty simplified. Do you mean that you want to expand it?

3. Nov 27, 2012

Polymath89

Sorry for not being clear, yes I want to expand the sum.

4. Nov 27, 2012

mathman

The sum looks almost like a binomial expansion.
net result e-(λ+μ)(λ+μ)w/w!.

5. Nov 28, 2012

Polymath89

Thank you very much.