Generalizations of Rogers–Ramanujan type identities

Recently the integral method was widely used to prove some Nahm problems. In the present paper we apply this method and the three-term transformation formula for \({}_2\phi _1\) $_2^{}{\varphi }_1$ series to establish some multi-sum Rogers-Ramanujan type identities with parameters. As special cases, we derive known Rogers-Ramanujan type identities, also find some new identities.