The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan
identities (Gordon 1961). It has a number of important applications in mathematical
physics (Fulman 1999).
The identity states
where ,
,
is complex with ,
and
(Andrews 1974; Andrews 1984, p. 111; Fulman 1999).
Andrews, G. E. "A Generalization of the Classical Partition Theorems." Trans. Amer. Math. Soc.145, 205-221, 1969.Andrews,
G. E. On
the General Rogers-Ramanujan Theorem. Providence, RI: Amer. Math. Soc., 1974.Andrews,
G. E. Encyclopedia
of Mathematics and Its Applications, Vol. 2: The Theory of Partitions.
Cambridge, England: Cambridge University Press, 1984.Fulman, J. "The
Rogers-Ramanujan Identities, The Finite General Linear Groups, and the Hall-Littlewood
Polynomials." Proc. Amer. Math. Soc.128, 17-25, 1999.Gordon,
B. "A Combinatorial Generalization of the Rogers-Ramanujan Identities."
Amer. J. Math.83, 393-399, 1961.Mc Laughlin, J.; Sills,
A. V.; and Zimmer, P. "Dynamic Survey DS15: Rogers-Ramanujan-Slater Type
Identities." Electronic J. Combinatorics, DS15, 1-59, May 31, 2008. http://www.combinatorics.org/Surveys/ds15.pdf.
,
,
is complex with 
,
and 
(Andrews 1974; Andrews 1984, p. 111; Fulman 1999).
