Bailey pair

A Bailey pair is a specific concept in the context of combinatorial identities and combinatorial number theory. It is related to the theory of basic hypergeometric series, which are a generalization of classical hypergeometric series. In particular, a Bailey pair consists of two sequences of numbers, usually denoted as \( (a_n) \) and \( (b_n) \), that satisfy certain combinatorial conditions and can be used to derive identities involving sums or series.