  We study the influence of a possible coherent component in the boson source
on the two-, three- and $n$-particle correlation functions in a generalized
core/halo type of boson-emitting source. In particular, a simple formula is
presented for the strengh of the $n$-particle correlation functions for such
systems. Graph rules are obtained to evaluate the correlation functions of
arbitrary high order. The importance of experimental determination of the 4-th
and 5-th order Bose-Einstein correlation function is emphasized.
