The right-hand side of the identity https://mathworld.wolfram.com/Andrews-GordonIdentity.html is a $q$-series $\frac{(q^i,q^{2k+1-i},q^{2k+1};q^k)_\infty}{(q;q)_\infty}$; 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".

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".

The right-hand side of the identity https://mathworld.wolfram.com/Andrews-GordonIdentity.html is a $q$-series $\frac{(q^i,q^{2k+1-i},q^{2k+1};q^k)_\infty}{(q;q)_\infty}$; is there a reference of its modularity? As the answer https://math.stackexchange.com/questions/1754128/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".

The right-hand side of the identity https://mathworld.wolfram.com/Andrews-GordonIdentity.html is a $q$-series $\frac{(q^i,q^{2k+1-i},q^{2k+1};q^k)_\infty}{(q;q)_\infty}$; 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".

The right-hand side of the identity https://mathworld.wolfram.com/Andrews-GordonIdentity.html is a $q$-series $\frac{(q^i,q^{2k+1-i},q^{2k+1};q^k)_\infty}{(q;q)_\infty}$; is there a reference of its modularity? As the answer https://math.stackexchange.com/questions/1754128/modular-forms-and-the-roger-ramanujan-identities-how suggests, the case of $k=i=2$ is not a trivial consequence of "expressing it as an eta-quotient".

The right-hand side of the identity https://mathworld.wolfram.com/Andrews-GordonIdentity.html is a $q$-series $\frac{(q^i,q^{2k+1-i},q^{2k+1};q^k)_\infty}{(q;q)_\infty}$; is there a reference of its modularity? As the answer https://math.stackexchange.com/questions/1754128/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".