Bailey’s Transform, Lemma, Chains and Tree

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In this paper we shall provide a brief survey of the work begun by L. J. Rogers and W. N. Bailey which has led to an iterative method for producing infinite chains of (q-series identities. Apart from providing the reader with leads to the study of previous accomplishments, we shall emphasize the importance of examination of the seminal works in order to discern topics open to further development. This will lead us directly to a new construct: the Bailey tree.