2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139331We unify and generalize formulas obtained by Campillo, Delgado and Gusein-Zade in their series of articles. Positive results are established for rational and minimally elliptic singularities. By examples and counterexamples we also try to find the `limits' of these identities. Connections with the Seiberg-Witten Invariant Conjecture and Semigroup Density Conjecture are discussed.24 pagesAlgebraic Geometry32C35;32S05;32S25;32S45Poincaré series associated with surface singularitiestext