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Power series recurrence relations

  1. Apr 11, 2009 #1
    1. The problem statement, all variables and given/known data
    In the following series':

    http://image.cramster.com/answer-board/image/cramster-equation-2009410014306337491927047975008434.gif

    According to my book, we only have a common range of summation here for n >= 2.

    Therefore we need to treat n = 0 and n = 1 separately.

    We thus write:

    [2r(r-1) + 3r - 1]c0 = 0

    and

    [2(r+1)r + 3(r+1)-1]c1 = 0

    My question is in both cases we ignored the last (4th) series to develop these two equations. How can we just ignore this power series?

    I imagine it must be because its summation begins at n=2 unlike the others, but why are we allowed to ignore it up until n = 2?

    Thanks!


    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Apr 12, 2009 #2

    tiny-tim

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    Hi IniquiTrance! :smile:

    (try using the X2 and X2 tags just above the Reply box :wink:)
    ah, but you're really writing:

    ([2r(r-1) + 3r - 1]c0 + 0)xr = 0

    and

    ([2(r+1)r + 3(r+1) -1]c1 + 0)xr+1 = 0,

    so you're not really ignoring the 4th sum at all, you're just not bothering to put in the zeros. :wink:

    Alternatively, think of the 4th sum as starting at n = 0 like the others, and with c-1 and c-2 defined as 0 :smile:
     
  4. Apr 13, 2009 #3
    Ah, ok much clearer now. Thank you!
     
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