The Andrews-Gordon identity is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities. It has a number of important applications in mathematical physics. The identity states sum_(n_1, ..., n_(k - 1)>=0) x^(N_1^2 + ... + N_(k - 1)^2 + N_i + ... + N_(k - 1))/((x)_(n_1) ...(x)_(n_(k - 1))) = product_(r = 1 r!=0, ± i (mod 2k + 1)) 1/(1 - x^r), where 1<=i<=k, k>=2, x is complex with left bracketing bar x right bracketing bar <1, and N_j = n_j + ... + n_(k - 1).

Göllnitz-Gordon identities | Gordon's partition theorem | Rogers-Ramanujan identities | Schur's partition theorem