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Programmable Multinomial Expansion

  1. Aug 14, 2009 #1
    Hello,

    How can we write a programmable multinomial expansion? I mean the summation over all non-negative integer indices, is somewhat difficult to program in Mathematica, at least for me. Is there any suggestions, please?


    I saw this formula at the Mathematica official website, but I didn't know how to interpret it:

    [tex]\left(a_1+a_2+\cdots+a_m\right)^n=\sum_{n_1,n_2,\dots,n_m=0}\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)\prod_{k=1}^ma_k^{n_k}[/tex]

    what does it mean [tex]n_1,n_2,\ldots,n_m=0[/tex]? and what is the delta function [tex]\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)[/tex]??

    Thanks in advance
     
    Last edited: Aug 14, 2009
  2. jcsd
  3. Aug 14, 2009 #2

    mathman

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    [tex]n_1,n_2,\ldots,n_m=0[/tex] means start the sum with all ni=0.
    [tex]\delta_{n;n_1+n_2+\cdots+n_m}\left(n;n_1,n_2,\ldots,n_m\right)[/tex] =1 when the sum of the ni=n and =0 otherwise.

    Note: For some reason I get an s where there should be ... In the checking before I submit it is correct???
     
    Last edited: Aug 14, 2009
  4. Aug 16, 2009 #3
    well, after we start all the indices from 0? Can you elaborate more, because I have no clear idea how to program this expansion in Mathematica.

    Thanks in advance
     
  5. Aug 16, 2009 #4

    mathman

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    I don't know anything about mathematica. Also (more important) the description you gave does not indicate what the upper limits of the summations for the m indices. In any case each ni goes from 0 to its upper limit.
     
  6. Aug 16, 2009 #5

    EnumaElish

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