  In this article we introduce a differential equation for the first order
correlation function $G^{(1)}$ of a Bose-Einstein condensate at T=0. The
Bogoliubov approximation is used. Our approach points out directly the
dependence on the physical parameters. Furthermore it suggests a numerical
method to calculate $G^{(1)}$ without solving an eigenvector problem. The
$G^{(1)}$ equation is generalized to the case of non zero temperature.
