  We investigate in this paper a generalization of Solomon-Terao formula for
central equidimensional subspace arrangements. We introduce generalized
Solomon-Terao functions based on the Hilbert-Poincar\'e series of the modules
of multi-logarithmic forms and logarithmic multi-residues. We show that as in
the case of hyperplane arrangements, these Solomon-Terao functions are
polynomial. We then prove that if the Solomon-Terao polynomial of the modules
of multi-residues satisfies a certain property, then this polynomial is related
to the characteristic polynomial of the subspace arrangement. In particular, we
prove that this generalized Solomon-Terao formula holds for any line
arrangement of any codimension.
