Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation

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.