2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133672This note extends Voiculescu's S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right interpretation of the S-transform in the case of vanishing mean, the usual formula makes perfectly good sense.Submitted to the Electronic Communications on ProbabilityOperator AlgebrasInformation TheoryProbability46L54 ; 15A52text