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We derive two general transformations for certain basic hypergeometric seriesfrom the recurrence formulae for the partial numerators and denominators of two$q$-continued fractions previously investigated by the authors. By thenspecializing certain free parameters in these transformations, and employingvarious identities of Rogers-Ramanujan type, we derive \emph{$m$-versions} ofthese identities. Some of the identities thus found are new, and some have beenderived previously by other authors, using different methods. By applyingcertain transformations due to Watson, Heine and Ramanujan, we derive stillmore examples of such $m$-versions of Rogers-Ramanujan-type identities.

Continued Fraction Proofs of $m$-versions of Some Identities of Rogers-Ramanujan-Slater Type