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A question on the orthogonal polynomial

  1. Sep 12, 2012 #1
    Dear All Friends,

    I am currently working on a project which needs some orthogonality
    integration formulae of Laguerre polynomials. I referred worlfram's math
    function site
    http://functions.wolfram.com/Polynomials/LaguerreL3/21/02/01/
    and get three seemingly useful ones.

    However, as very natural exercises, when I made tests by setting
    (p=1,alpha=lambda+1,beta=lambda,m=n) in the third equation of the
    above web-page and try to get the first one, I always cannot accomplish
    the goal. So I suspect the inter-consistances of the three integration formulae
    in the above web-page.

    Is here someone professional in orthogonality polynomials and would like
    to resolve my suspicious? Or can here someone recommend me some
    materials so that I can learn and derive out the desired integration formulae
    by myself?

    Thank you very much!
     
  2. jcsd
  3. Sep 14, 2012 #2
    Check out Dixon's identity and the rules for the Gamma function (basically that it's just factorial for integer arguments) and you will find your way from eq.3 to eq.1
     
  4. Sep 17, 2012 #3
    Thank you very much! I worked it out just as you suggested!
     
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