  A new method for studying the many-body response functions is elaborated and
first applied to the $^3$He longitudinal response. An integral transform of the
response function is calculated from the bound-state-type equations for several
versions of the N-N force. The equations are solved with the help of the
hyperspherical expansion. The final-state interaction is completely taken into
account. The results are compared with the integral transform of the
experimental response function for 250 MeV/c$\leq q \leq 500$ MeV/c. The
difference amounts to 20-25\% with the experimental response substantially
exceeding the theoretical one in the low-energy region.
