The first and the third authors obtained a minor-summation formula of
Pfaffian, which expresses a weighted sum of miners of any rectangular
matrix in terms of a single Pfaffian. In this paper, as an application
of this minor-summation formula, we give a new proof of Littlewood's
formulas with additional parameters and generalize them for the classi
cal groups. (C) 1996 Academic Press, Inc.