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How to prove this

  1. Nov 18, 2009 #1
    given a set of orthogonal polynomials with respect to a certain measure w(x)

    [tex] \int_{a}^{b}dx w(x) P_{n} (x)P_{m} (x) = \delta _{n,m}h_{n} [/tex]

    how can anybody prove that exists a certain M+M Hermitian matrix so

    [tex] P_{m} (x)= < Det(1-xM)> [/tex] here <x> means average or expected value of 'x'

    if we knew the set of orthogonal polynomials [tex] P_{m} (x) [/tex] for every 'm' and the measure w(x) , could we get the expression for the matrix M ??
     
  2. jcsd
  3. Nov 18, 2009 #2
    Your equation doesn't make much sense to me. How about providing an example. A particular orthogonal system and the corresponding matrix.
     
  4. Dec 31, 2009 #3
    Looks like we got ourselves a troll.
     
  5. Jan 5, 2010 #4
    Interesting way to react to posts that do not tickle the own ears - delete them. You guys are not seekers of truth. Ibn al Haytham would be ashamed for you all.
     
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