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