# Conditional multivariate normal distribution

If $X = [X_1,\dots,X_n]$ is follows a multivariate normal distribution $\mathcal{N}(\mu,\Sigma)$, are there any (closed form) results known for the distribution of $[X_1,\dots,X_i \mid l_{i+1} < X_{i+1} < u_i ,\dots, l_n < X_n < u_n]$?