50 Years of Bailey’s Lemma

By S. Ole Warnaar. 2009

122 citations recorded by the source corpus.

Half a century ago, The Proceedings of the London Mathematical Society published W. N. Bailey’s influential paper Identities of the Rogers-Ramanujan type [16]. The main result therein, which was inspired by Rogers’ second proof of the Rogers-Ramanujan identities [49] (and also [48,28,15]), is what is now known as Bailey’s lemma. To celebrate the occasion of the lemma’s fiftiest birthday we present a history of Bailey’s lemma in 5 chapters (or rather sections), covering (i) Bailey’s work, (ii) the Bailey chain (iii) the Bailey lattice (iv) the Bailey lemma in statistical mechanics, and (v) conjugate Bailey pairs.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/d1caee209bf3c6a0615edf32a453eecb38591bb5

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Citations in the corpus

The WP‐Bailey Tree and its Implications (2001, result): “Research by the first author was partially supported by NSF grant DMS-9206993, and research by the second author was supported in part by NSF grant DMS-0088975.”
Extensions of the well-poised and elliptic well-poised Bailey lemma (2003, methodology): “For more details we refer to the reviews [1,2, 22 ].”
A Bailey lattice (2003, methodology): “Several authors [1, 9, 13, 15] have extended the Bailey chain by introducing techniques for obtaining new Bailey pairs with respect to a/q from Bailey pairs with respect to a.”