how can an integration like: $\int_\mathbb{C}f(|z|^2)dz$ be perfomerd? Function $f(|z|^2)$ is a kind of entropy function, resulted from circular symmetric complex gaussian probability densityfunction. The problem is that integrand is a realfunction, and can be analytical only in limited numbers of point in plane. I have only seen the result of this integration in a paper, and now have faced a similar one. Thanx for any help.

how can an integration like: $\int_\mathbb{C}f(|z|^2)dz$ be perfomerd? Function $f(|z|^2)$ is a kind of entropy function, resulted from circular symmetric complex gaussian probability density function. The problem is that integrand is a real function, and can be analytical only in limited numbers of point in plane. I have only seen the result of this integration in a paper, and now have faced a similar one. Thanx for any help.