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Integrals of products of Hermite polynomials

  1. Feb 7, 2012 #1
    Hey people,

    I need to calculate inner product of two Harmonic oscillator eigenstates with different mass. Does anybody know where I could find a formula for
    [itex]
    \int{ H_n(x) H_m(\alpha x) dx}
    [/itex]

    where [itex]H_n, H_m[/itex] are Hermite polynomials?
     
  2. jcsd
  3. Feb 8, 2012 #2

    cgk

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    Science Advisor

    Here, for example:
    http://www.wolframalpha.com/input/?i=Integrate[HermiteH[3%2C+x]*HermiteH[5%2C+x%2F3]%2C+x]

    (use {x,-Infinity,+Infinity} for the last argument to get a definite integral, although this does not actually converge for this example)
     
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