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Problem with Sumations

  1. Feb 10, 2006 #1
    I have a hard time trying to figure it out how to derive the following sumations:

    We know that:
    P(z) = Sumation from j=0 to Infinity of [(Pj * (z^j)]
    and
    Q(z) = Sumation from j=0 to Infinity of [(Kj * ((z^j)]

    Where j is a subindex for P and K, and a power for z.


    Sumation from j=0 to Infinity of [ Sumation from i=0 to j+1 of [(z^j) * Pi * Kj-i+1] ]

    Where i and j are a subindices for P and K, and a power for z.



    I know that I have to play with the indices, but I have no clue. Any advice??
     
  2. jcsd
  3. Feb 11, 2006 #2

    mathman

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    I may be missing something, but I can't see what your question is?
     
  4. Feb 12, 2006 #3
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    Yes, you are right.
    From the information above, it has to be simplified to:
    [ (1/z) * P(z) * Q(z) ] - [ (1/z) * Po * Q(z) ]

    The author of the book does not give much more information about how he derived this equation, but he says is trivial.
     
  5. Feb 12, 2006 #4

    mathman

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    The basic trick is to switch the order of summation. Then you will have two parts. The main part has i=1,inf with j=i-1,inf. The other part has i=0 with j=0,inf. For the main part let n=j-i+1 (replacing j), then n=0,inf. Put it all together and you should get the required answer.
     
  6. Feb 12, 2006 #5
    Sorry

    I am sorry, but I still do not get it.
     
  7. Feb 13, 2006 #6

    mathman

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    Do you understand switching the order of summation?
    Do you see the result of switching?
    Do you understand the change of variables (n=)?
     
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