A general $q$-series transformation and its applications to multi-sum Rogers-Ramanujan-Slater identities

In the present paper, we establish a general transformation for $q$-series which contains L. Wang et al’s transformation involved in Nahm series. As direct applications, some concrete new transformation formulas for the ${}_{r+1}{\phi }_r$ series as well as $q$-identities of multi-sum Rogers-Ramanujan-Slater type are presented.