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Legendre Series Expansion

  1. Mar 4, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the n+1 and n-1 order expansion of [itex]\stackrel{df}{dy}[/itex]

    2. Relevant equations

    (n+1)Pn+1 + nPn-1 = (2n+1)xPn

    ƒn = [itex]\sum[/itex] CnPn(x)

    Cn = [itex]\int[/itex] f(x)*Pn(u)

    3. The attempt at a solution

    I know you can use the recursion relation for Legendre Polynomials once you combine Cn with the summation to get two terms one for fn+1 and one for fn-1.

    [itex]\int[/itex] (n+1)Pn+1(x)dxPn(x)


    [itex]\int[/itex] nPn-1(x)dxPn(x)

    At this step I'm not exactly sure as what to do. I don't use Legendre Series very often so I tend to get confused by them. Do you just use the simple 2/(2n+1) solution from the orthogonality property and use n = n+1 or n = n-1?

    Thanks for any help in advance.
    Last edited: Mar 4, 2014
  2. jcsd
  3. Mar 12, 2014 #2
    I don't understand your question. Can you clarify it?
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