Andrews-Gordon Type Series for Capparelli's and G\"{o}llnitz-Gordon Identities

We construct Andrews-Gordon type evidently positive series as generating functions for the partitions satisfying the difference conditions imposed by Capparelli’s identities and G"{o}llnitz-Gordon identities. The construction involves building base partitions, and move parts around subject to certain rules. Some missing cases are also considered, but no new identities are given.