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Summation with Factorial

  1. Nov 27, 2012 #1
    I need to simplify this expression and I don't know how to deal with the factorials in the sum

    [tex]e^{-(\lambda + \mu)}\sum_{k=0}^w \frac{\lambda^k \mu^{(w-k)}}{k!(w-k)!}[/tex]

    Can anybody give me a hint on how to sum over the factorials?
  2. jcsd
  3. Nov 27, 2012 #2


    Staff: Mentor

    This is already pretty simplified. Do you mean that you want to expand it?
  4. Nov 27, 2012 #3
    Sorry for not being clear, yes I want to expand the sum.
  5. Nov 27, 2012 #4


    User Avatar
    Science Advisor

    The sum looks almost like a binomial expansion.
    net result e-(λ+μ)(λ+μ)w/w!.
  6. Nov 28, 2012 #5
    Thank you very much.
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