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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.