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Legendre equation , the Bessel equation and Sturm Liouville equation

  1. Dec 28, 2012 #1

    Show that the Legendre equation as well as the Bessel equation for n=integer are Sturm Liouville equations and thus their solutions are orthogonal.


    How I can proove that ..?

    :(
     
    Last edited: Dec 28, 2012
  2. jcsd
  3. Dec 28, 2012 #2
    Can you put it in sturm-liouville form?
     
  4. Dec 28, 2012 #3
    Yes ...

    see . this is the form of Sturm Liouville


    561338810.png



    and this table help me

    890517201.png


    i found the mathematical explain for bessel .

    but i don't know how i can prove thier solutions are orthogonal ..!


    can you help me :confused:
     
    Last edited: Dec 28, 2012
  5. Dec 28, 2012 #4
    Did you post the problem exactly? If so, as I interpret it, you do not need to prove that yourself. It is well known that the solutions to sturm-liouville problems are orthogonal and the proof can be found in any mathematical methods book.
     
  6. Dec 28, 2012 #5
    yea

    i understand that hour before .. i wasn't have enough information about sturm-liouville

    or maybe my brain stopped :tongue:



    thanks :)
     
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