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Using Lie theory, Stefano Capparelli conjectured an interestingRogers-Ramanujan type partition identity in his 1988 Rutgers Ph.D. thesis. Thefirst proof was given by George Andrews, using combinatorial methods. Later,Capparelli was able to provide a Lie theoretic proof.  Most combinatorial Rogers-Ramanujan type identities (e.g. theG\"ollnitz-Gordon identities, Gordon's combinatorial generalization of theRogers-Ramanujan identities, etc.) have an analytic counterpart. The mainpurpose of this paper is to provide two new series representations for theinfinite product associated with Capparelli's conjecture. Some additionalrelated identities, including new infinite families are also presented.

On Series Expansions of Capparelli's Infinite Product