The right-hand side of the identity https://mathworld.wolfram.com/Andrews-GordonIdentity.html is a $q$-series $\frac{(q^i,q^{2k+1-i},q^{2k+1};q^{2k+1})_\infty}{(q;q)_\infty}$; is there a reference of its modularity? As Somos's answer to Modular forms and the Roger-Ramanujan identities: How?? suggests, the case of $k=i=2$ is already not a trivial consequence of "expressing it as an eta-quotient".
$\begingroup$
$\endgroup$
1
-
$\begingroup$ Your link for "the answer" went to a question; but the question has only one answer, so I assume that was what you meant. I edited accordingly. $\endgroup$– LSpiceCommented Jun 24, 2023 at 23:33
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
This kind of infinite product has been studied by Klein and Siegel (mentioned in the Remark of p3 of Griffin--Ono--Warnaar). For a detailed description of its modularity, see Robins, Generalized Dedekind $\eta$-products, Contemporary Mathematics (196), 1994, 119-128.