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Proof of orthogonality of associated Legendre polynomial

  1. Sep 30, 2009 #1
    I want to prove orthogonality of associated Legendre polynomial.

    In my text book or many posts,
    [tex]\int^{1}_{-1} P^{m}_{l}(x)P^{m}_{l'}(x)dx = 0 (l \neq l')[/tex]
    is already proved.

    But, for upper index m,
    [tex]\int^{1}_{-1} P^{m}_{n}(x)P^{k}_{n}(x)\frac{dx}{ ( 1-x^{2} ) } = 0 (m \neq k)[/tex]
    is not proved.

    So, I tried to prove it using same method for the first case.
    But I could not prove it.
    Will anyone show me a hint or online reference?
    Last edited: Sep 30, 2009
  2. jcsd
  3. Sep 30, 2009 #2
    plug in the formulas and do the integral. what have you done so far?
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