Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook