In this note, the universality of a sequence of operators associated to the partial sums of the Taylor series of a holomorphic function is investigated. The emphasis is put on the fact that the Taylor series are evaluated at a prescribed point and the variable is the center
of the expansion. The dynamics of the sequence of operators linked to the partial sums of a power series that is not generated by an entire function is also studied.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). Españ
