ABSTRACT
The most powerful aspect of Bailey’s lemma, the fact that any Bailey pair generates another (see (2.32), (2.33)), and therefore infinitely many, was not noticed by Bailey. This self-replicating aspect of Bailey pairs, known as the Bailey chain, was discovered in its full generality by Andrews [And84]. Independently, the iterative potential of Bailey’s lemma was observed by Peter Paule [Pau82, Pau85, Pau87].
