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Eigenfunction expansion in Legendre polynomials

  1. Aug 25, 2008 #1
    1. The problem statement, all variables and given/known data

    How to use eigenfunction expansion in Legendre polynomials to find the bounded solution of
    (1-x^2)f'' - 2xf' + f = 6 - x - 15x^2 on -1<= x <= 1

    2. Relevant equations

    eigenfunction expansion

    3. The attempt at a solution

    [r(x)y']' + [ q(x) + λ p(x) ] = f(x)
    In this case, r = 1-x^2 , q = 1 , p = 0 , f = 6 - x -15 x^2 , r(-1) = r (1) = 0

    Thanks for any help!
     

    Attached Files:

    • q.bmp
      q.bmp
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  2. jcsd
  3. Aug 26, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    First what are the eigenfunctions you want to use? In other words, what are the solutions to Legendre's equation.
     
  4. Sep 3, 2008 #3
    I have the same problem.

    the attachment from hi10 is what i was thinking.

    Does anyone know what u(x) is in hi10's post for determining what an is?
     
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