Some $q$-transformation formulas and Rogers-Ramanujan type identities

Abstract

In this paper, we explore the role that Liu's transformation formula can play in discovering Rogers-Ramanujan type identities. Specifically, we combine Liu's transformation formula with other $q$-series summations to derive a series of parameterized identities. Thereafter, through careful selection of these parameters, we obtain $75$ Rogers-Ramanujan type identities from Slater's list, and uncover several new Rogers-Ramanujan type identities.