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Multinomial expansion

  1. Apr 24, 2015 #1

    I would like to express the following formula in terms of a straightforward multinomial expansion:


    Any help would be useful.
  2. jcsd
  3. Apr 24, 2015 #2


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    Would you explain the notation? What is $x(i)$, are you multiplying the two sums?
  4. Apr 24, 2015 #3
    Ok, I redifine the expression:

    (Σ^{m}_{i=0}x^i*Σ^{i}_{j=0}y^j)^n, where x,y are nonnegative real numbers and m,n are nonnegative integers
  5. Apr 24, 2015 #4


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    It is easier to read as latex. I don't understand what you are looking for. My guess:

    y sum is [itex]\frac{1-y^{i+1}}{1-y}[/itex]

    You can now get i sum to get [itex](\frac{f(x)-yf(xy)}{1-y})^n\ where\ f(u)=\frac{1-u^{m+1}}{1-u}[/itex]
    Last edited: Apr 24, 2015
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