| Summary: | The Rogers-Ramanujan identities can be stated either analytically or combinatorially. Each viewpoint has led to its own generalizations. On the analytic side, there is the work of Watson, Bailey, Slater, Singh, Andrews and others. On the combinatorial side is the work of Schur, Gordon, Göllnitz, Andrews and others. In this paper, two very general theorems will be proved; the first of these is an analytic statement and contains as special cases many of the known analytic generalizations; the second is a combinatorial statement which contains as special cases many of the combinatorial generalizations. Most significantly, the connection between the analytic and combinatorial theorems will be demonstrated.
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