$\chi^2$ distance and multivariate gaussian distribution

Question

I want to know how to write the $\chi^{2}$ distance between two multivariate Gaussian distributions $f$ and $g$ in terms of their parameters only. The parameters of $f$ is the vector $\mu_{1}$ and a covariance matrix $\Sigma_{1}$. The parameters of $g$ is the vector $\mu_{2}$ and a covariance matrix $\Sigma_{2}$.