  The colored Jones polynomial is a $q$-polynomial invariant of links colored
by irreducible representations of a simple Lie algebra. A $q$-series called a
tail is obtained as the limit of the $\mathfrak{sl}_2$ colored Jones
polynomials $\{J_n(K;q)\}_n$ for some link $K$, for example, an alternating
link. For the $\mathfrak{sl}_3$ colored Jones polynomials, the existence of a
tail is unknown. We give two explicit formulas of the tail of the
$\mathfrak{sl}_3$ colored Jones polynomials colored by $(n,0)$ for the
$(2,2m)$-torus link. These two expressions of the tail provide an identity of
$q$-series. This is a knot-theoretical generalization of the Andrews-Gordon
identities for the Ramanujan false theta function.
