Department of Statistics and Computation, Universidad Autonoma Agraria Antonio Narro, Buenavista, Saltillo, Coahuila, MexicoDepartment of Basic Sciences, Universidad de Medellín, Carrera 87 No.30-65, of. 5-103, Medellín, Colombia2023-11-212023-11-21http://repository-salesiana.heoq.net/handle/123456789/227539An extension of the well known matrix Kummer relation of Herz (1955) is proposed in this paper by assuming a general model which admits a Taylor expansion. Under certain conditions of the involved parameters, the addressed generalisation can be used for deriving efficiently computable matrix variate densities based on non Gaussian models, avoiding some open problems of the literature in the context of shape theory and other related fields. © Publisherinfo:eu-repo/semantics/restrictedAccessinfo:eu-repo/semantics/restrictedAccessHypergeometric functionMatrix Kummer relationsZonal polynomials.Article