Dedekind’s \(\eta \)-function and Rogers-Ramanujan identities. (English) Zbl 1234.05040

Warnaar, S. Ole; Zudilin, Wadim

Bull. Lond. Math. Soc. 44, No. 1, 1-11 (2012).

Summary: We prove a \(q\)-series identity that generalizes Macdonald’s \(A_{2n}^{(2)} \eta \)-function identity and the Rogers-Ramanujan identities. We conjecture our result to generalize even further to also include the Andrews-Gordon identities.

MSC:

05A19	Combinatorial identities, bijective combinatorics
05E05	Symmetric functions and generalizations
11F20	Dedekind eta function, Dedekind sums
33D67	Basic hypergeometric functions associated with root systems

Keywords:

Andrews-Gordon identities; Macdonald’s \(A_{2n}^{(2)} \eta \)-function identity