# §17.12 Bailey Pairs

## ¶ Bailey Pairs

A sequence of pairs of rational functions of several variables , , is called a Bailey pair provided that for each

## ¶ Strong Bailey Lemma

When (17.12.5) is iterated the resulting infinite sequence of Bailey pairs is called a Bailey Chain.

The Bailey pair that implies the Rogers–Ramanujan identities §17.2(vi) is:

The Bailey pair and Bailey chain concepts have been extended considerably. See Andrews (2000, 2001), Andrews and Berkovich (1998), Andrews et al. (1999), Milne and Lilly (1992), Spiridonov (2002), and Warnaar (1998).