Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Multinomial expansion

  1. Apr 24, 2015 #1
    Hi,

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

    (Σ^{m}_{i=0}x(i)*Σ^{i}_{j=0}x(i,j))^n

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

    WWGD

    User Avatar
    Science Advisor
    Gold Member

    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

    mathman

    User Avatar
    Science Advisor
    Gold Member

    [itex](Σ^{m}_{i=0}x^i*Σ^{i}_{j=0}y^j)^n[/itex]

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Multinomial expansion
  1. Expansion of functions (Replies: 8)

  2. Log expansion (Replies: 1)

  3. Series expansion (Replies: 1)

Loading...