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Legendre Polynomial and Rodrigues' Formula

  1. Oct 30, 2012 #1
    I am reading Jackson's electrodynamics book. When I went through the Legendre polynomial, I have a question.

    In the book, it stated that from the Rodrigues' formula we have
    Consider only the odd terms
    How to obtain this equation and how can I obtain the equation for even terms?

    Thanks in advance.
  2. jcsd
  3. Oct 30, 2012 #2


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    The general formula (irrespective of l even or odd) is


    or set [itex] \sigma=0[/itex] in the formula (807) 7.126.1 in Gradshteyn-Ryzhik.

    The whole proof for l=odd is in Bell, W.W."Special Functions for Scientists and Engineers", (VanNostrand, 1967) as Example 2 on Page 86.

    You can make the proof by yourself with help of the fully solved case l=odd by making the necessary changes in the proof already given.
  4. Nov 2, 2012 #3

    Meir Achuz

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    The formula is more easily derived using the generating function.
    The integral equals 1 for l=0, and is zero for all higher even l.
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