  The electron transport through a three-terminal single-molecular transistor
(SMT) is theoretically studied. We find that the differential conductance of
the third and weakly coupled terminal versus its voltage matches well with the
spectral function versus the energy when certain conditions are met.
Particularly, this excellent matching is maintained even for complicated
structure of the phonon-assisted side peaks. Thus, this device offers an
experimental approach to explore the shape of the phonon-assisted spectral
function in detail. In addition we discuss the conditions of a perfect
matching. The results show that at low temperatures the matching survives
regardless of the bias and the energy levels of the SMT. However, at high
temperatures, the matching is destroyed.
