Thread: What is the product of a cauchy and a normal distribution?

let Z=XY, X is cauchy distribuion,Y is normal distribuion. X and Y is independent.I want to find the distribution of Z.
how could I get the distribution of z in analytic expression or can we prove the integration is non-integrable?
can you give me some advice?
thanks!

perhaps you can find the joint distribution of x and y with a double integral.

or there is some good information on this mathworld page

Distribution Function -- from Wolfram MathWorld

sorry cant be more help but im not sure what to do. but this is where id probably start