Is there a table of Abel transforms for Gaussian distributions available?

[Mr Boom]

Hello. I'm wondering if anyone has a table of transforms showing the result of an Abel transform on a Gaussian distribution. I have been unable to find the solution to this. Many thanks for any help. I'm reconstructing an an image from a picture that fits a Gaussian very well, hence I'm hoping to just use an analytical solution.

Dave

 

[Mr Boom]

and the answer is...

So I found the solution described as f(r) -> f(x):

exp(-r²/2σ²) -> (2π)^1/2σ*exp(-x²/2σ²)

The added constant does not change the the value of sigma so, which doesn't make sense to me. When viewing the line itegral, shouldn't the distribution appear more narrow?