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Legendre Polynomial solutions

  1. May 19, 2005 #1
    I have a problem where I am given the Legendre equation and have been told 1 solution is u(x). It asks me to obtain an expression for the second solution v(x) corresponding to the same value of l.
    I think it requires Sturm Liouville treatment but don't have a clue how to begin.
    Please HELP!
  2. jcsd
  3. May 19, 2005 #2


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  4. May 19, 2005 #3


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    More generally, if you have a known solution, u(x) to a differential equation, Taking
    y(x)= u(x)v(x), where v(x) is an unknown function, and plugging into the equation,you get an equation of order one lower for v. In particular, if you know one solution to a second order equation, this will give you a first order equation for an independent solution v(x).
  5. May 19, 2005 #4
    OK so I've skimmed that page and its confirmed what I've got in my lecture notes (albeit in a more complex manner!) :surprised
    The question remains though, how would I be expected to answer the question, given that this question is only worth 9 marks out of a possible 25 on my exam sheet?!
    Surely its asking for something a lot more direct, and I'm still in the dark as to how to begin and what to do.........
  6. May 19, 2005 #5


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    Take Halls' advice and do what he said.I'm sure u'll get the second indep.solution.

  7. May 19, 2005 #6
    Yes, sorry I was typing that reply whilst Hall's was posted.
    Thanks for your help, I think I know where to go from here
  8. Feb 8, 2010 #7
    Can somebody help me in deriving legendre differential function using its generating function
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