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Tricky supergaussian integral

  1. Nov 4, 2011 #1
    I am trying to solve the integral of a supergaussian multiplied by a Rician distribution.

    Basically, I am trying to solve an integral of the form

    [itex]
    \int_0^{\infty}e^{-ax^4}e^{-bx^2}xI_0(cx)dx
    [/itex]

    I have no particular reason to believe this has a closed form.
    However, I have solved a normal gaussian times a Rician; however, that involved completing the square and the integral being a valid Rician, thus summing to 1 and leaving multipliers, which will not generalize to higher order.

    I have tried a few methods, including substituting u = x^2 and then Laplace transform.
     
  2. jcsd
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