Given: $Z=\sqrt{X^2+Y^2}, X\sim N(\mu_x,\sigma_x^2), Y\sim N(\mu_y,\sigma_y^2)$
What is the expected value of $Z$?
I'm specifically looking for the case where the $\mu_i$ are non-zero and $\sigma_i$ are different, so it's neither a generalized Chi nor a non-central Chi, as far as I could tell.
A more general form for the norm of N normal variables would also be nice.