  Using the theory of intertwining operators for vertex operator algebras we
show that the graded dimensions of the principal subspaces associated to the
standard modules for $\hat{\goth{sl}(2)}$ satisfy certain classical recursion
formulas of Rogers and Selberg. These recursions were exploited by Andrews in
connection with Gordon's generalization of the Rogers--Ramanujan identities and
with Andrews' related identities. The present work generalizes the authors'
previous work on intertwining operators and the Rogers--Ramanujan recursion.
