  We derive an analytic expression for the zero temperature Fourier transform
of the density-density correlation function of a multicomponent Luttinger
liquid with different velocities. By employing Schwinger identity and a
generalized Feynman identity exact integral expressions are derived, and
approximate analytical forms are given for frequencies close to each component
singularity. We find power-like singularities and compute the corresponding
exponents. Numerical results are shown for the case of three components.
