## 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].

### MSC:

 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$ 05A17 Combinatorial aspects of partitions of integers

Bailey chain