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We give "hybrid" proofs of the $q$-binomial theorem and other identities. Theproofs are "hybrid" in the sense that we use partition arguments to prove arestricted version of the theorem, and then use analytic methods (in the formof the Identity Theorem) to prove the full version. We prove three somewhatunusual summation formulae, and use these to give hybrid proofs of a number ofidentities due to Ramanujan. Finally, we use these new summation formulae togive new partition interpretations of the Rogers-Ramanujan identities and theRogers-Selberg identities.

Hybrid Proofs of the $q$-Binomial Theorem and other identities