  Formulas for the expansion of arbitrary invariant group functions in terms of
the characters for the Sp(2N), SO(2N+1), and SO(2N) groups are derived using a
combinatorial method. The method is similar to one used by Balantekin to expand
group functions over the characters of the U(N) group. All three expansions
have been checked for all N by using them to calculate the known expansions of
the generating function of the homogeneous symmetric functions. An expansion of
the exponential of the traces of group elements, appearing in the finite-volume
gauge field partition functions, is worked out for the orthogonal and
symplectic groups.
