  There exist a number of well known multiplicative generating functions for
series of Schur functions. Amongst these are some related to the dual Cauchy
identity whose expansion coefficients are rather simple, and in some cases
periodic in parameters specifying the Schur functions. More recently similar
identities have been found involving expansions in terms of characters of the
symplectic group. Here these results are extended and generalised to all
classical Lie groups. This is done through the derivation of explicit
recurrence relations for the expansion coefficients based on the action of the
Weyl groups of both the symplectic and orthogonal groups. Copious results are
tabulated in the form of explicit values of the expansion coefficients as
functions of highest weight parameters. An alternative approach is then based
on dual pairs of symplectic and/or orthogonal groups. A byproduct of this
approach is that expansions in terms of spin orthogonal group characters can
always be recovered from non-spin cases.
