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Integral involving Hermite polynomials

  1. Jan 5, 2009 #1

    Is there any way of calculating the integral of H_n(x) * H_m(x) * exp(-c^2 x^2) with x going from -infinity to +infinity and c differs from unity. I'm aware that c=1 is trivial case of orthogonality but I'm really having a problem with the general case. (I should say that this isn't a homework assignment, rather curiosity).

    Any ideas?

  2. jcsd
  3. Jan 5, 2009 #2
    I don't believe that there is any nice formula for that. However, notice that you can calculate that explicitly if you fix some small indexes n and m. It could be, that if you do that, then some pattern becomes visible. So why not calculate it with (n,m)=(1,1), (0,2), (1,3), (2,2), (2,4) and see what happens?
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