- #1
boxkar
- 1
- 0
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
<br /> \int_0^{\infty}e^{-ax^4}e^{-bx^2}xI_0(cx)dx<br />
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.
Basically, I am trying to solve an integral of the form
<br /> \int_0^{\infty}e^{-ax^4}e^{-bx^2}xI_0(cx)dx<br />
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.
