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Bailey’s transform, lemma, chains and tree. (English) Zbl 1005.33005
Bustoz, Joaquin (ed.) et al., Special functions 2000: current perspective and future directions. Proceedings of the NATO Advanced Study Institute, Tempe, AZ, USA, May 29-June 9, 2000. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 30, 1-22 (2001).
This is an overview of Bailey chains, an important tool in the discovery and proof of $q$-series identities. The author gives examples of one- and multi-dimensional Bailey chains as well as a recent variation he calls the $WP$-Bailey chain because it is based on Bailey’s proof of an identity between two very well-poised basic hypergeometric series. For the entire collection see [Zbl 0969.00053].

33D15Basic hypergeometric functions of one variable, ${}_r\phi_s$
05A17Partitions of integers (combinatorics)
Bailey chain