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Re-write the Equation

  1. Jun 12, 2009 #1

    I have the following equation:

    [tex]f(x)=\sum_{r=m}^{M_B}\,\sum_{i=0}^{M_B-r}\,\sum_{j=0}^{r+i}\,\sum_{k=0}^{j(N_B-1)}(-1)^{i+j}{M_B\choose r}{M_B-r\choose i}{r+i\choose j}\left(\frac{x}{C}\right)^k\,e^{jx/C}[/tex]

    and I want to write it in the form of [tex]f(x)=1+R(x)[/tex]

    [tex]m[/tex] will be any number from 1 up to [tex]M_B[/tex], and [tex]f(x)=1-e^{x/C}[/tex] for [tex]M_B=N_B=1[/tex].

    Can anyone help me, please? Because I am not sure about the limits when extracting some values of them.

  2. jcsd
  3. Jun 12, 2009 #2


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    Gold Member

    [tex]f(x)=1+\sum_{r=m}^{M_B-1}\,\sum_{i=1}^{M_B-r}\,\sum_{j=1}^{r+i}\,\sum_{k=1}^{j(N_B-1)}(-1)^{i+j}{M_B\choose r}{M_B-r\choose i}{r+i\choose j}\left(\frac{x}{C}\right)^k\,e^{jx/C}[/tex].
  4. Jun 12, 2009 #3
    But this doesn't give us [tex]f(x)=1-e^{x/C}[/tex] for [tex]M_B=N_B=1[/tex]. And we have the problem for the last summation where the limits will be 1 to 0, how to handle this problem?
  5. Jun 12, 2009 #4
    Where are the mathematician? I really need this one. Please help if you can.
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