2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161756Using the combinatorics of non-crossing partitions, we construct a conditionally free analogue of the Voiculescu's S-transform. The result is applied to analytical description of conditionally free multiplicative convolution and characterization of infinite divisibility.Operator AlgebrasCombinatorics46L53; 05A18, 60E07text