  We derive explicit expressions for dynamical correlations of the field and
density operators in the Lieb-Liniger model, within an arbitrary eigenstate
with a small particle density ${\cal D}$. They are valid for all space and time
and any interaction strength $c>0$, and are the leading order of an expansion
in ${\cal D}$. This expansion is obtained by writing the correlation functions
as sums over form factors when formally decomposed into partial fractions.
