2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141846We give an elementary proof of the existence of an asymptotic expansion in powers of $k$ of the Bergman kernel associated to $L^k$, where $L$ is a positive line bundle. We also give an algorithm for computing the coefficients in the expansion.revised, mainly stylistic changesComplex Variables32A25text