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

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


    and this table help me


    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

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

    or maybe my brain stopped :tongue:

    thanks :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook