2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139368The volume conjecture and its generalization state that the series of certain evaluations of the colored Jones polynomials of a knot would grow exponentially and its growth rate would be related to the volume of a three-manifold obtained by Dehn surgery along the knot. In this paper, we show that for the figure-eight knot the series converges in some cases and the limit equals the inverse of its Alexander polynomial.13 pagesGeometric Topology57M27;57M25text