$q$-WZ-Theory and Bailey Chains

Many combinatorial identities can be formulated in terms of $q$-hypergeometric sums, for instance, the celebrated Rogers-Ramanujan identities from additive number theory. Identities of such type can be constructed iteratively from simpler ones, i.e., by proceeding along Bailey chains. Another construction mechanism, different from this classical one, arises within the context of $q$-WZ-theory. For instance, as a by-product of computer proofs, one automatically obtains the so-called "dual" identities. The talk gives a short tutorial introduction and discusses various relations between these concepts.