One-parameter generalizations of Rogers–Ramanujan type identities

Using the recursions satisfied by the polynomials which converge to the right-hand sides of the Rogers–Ramanujan type identities given by Sills (2003) [16], and a determinant method presented in Ismail et al. (2000) [8], we obtain many new one-parameter generalizations of the Rogers–Ramanujan type identities, such as a generalization of the analytic versions of the first and second Göllnitz–Gordon partition identities, and generalizations of the first, second, and third Rogers–Selberg identities.