  The dipole flexoelectric (FE) polarization in liquid crystals is derived in
the thermodynamic limit at small distortions and small density. General
microscopic expressions for the FE coefficients are obtained in the case of the
uniaxial and biaxial nematic phases composed of C_2v molecules. The expressions
involve the one-particle distribution function and the potential energy of
two-body short-range interactions. In the case of the biaxial nematic phase,
six basic deformations produce FE polarization but there are only five
independent FE coefficients.
