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Legendre polynomials

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Integrate the expression
    Pl and Pm are Legendre polynomials

    2. Relevant equations




    3. The attempt at a solution
    Suppose that solution is equal to zero.
     

    Attached Files:

  2. jcsd
  3. Jan 5, 2012 #2
    What properties do you know about Legendre Polynomials? If you can use the orthogonal properties that are listed in the article on Legendre polynomials in wikipedia, then integration by parts should do the trick.
     
  4. Jan 5, 2012 #3
    But, how make Pm'(x) I don't understand(recurrent differentiation formula?)
     
  5. Jan 5, 2012 #4
    Under the orthogonality section in the wikipedia article on Legendre polynomials, you find the identity
    [itex]\displaystyle \frac{d}{dx}\left[(1-x^2)\frac{d}{dx}P(x)\right] = -\lambda P(x)[/itex]
    where the eigenvalue [itex]\lambda[/itex] corresponds to [itex]n(n+1).[/itex]
    I suppose [itex]P(x)=P_n(x)[/itex] for any [itex]n[/itex], but I'm not sure though. If this is the case, and you know this property, then integration by parts should do the trick.
     
  6. Jan 6, 2012 #5
    Thanks for help, I succeeded to do job.
     
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