Power Series Methods and Multisummability

We recall the notion of a power series summability method and show, using results of W. Balser and A. Beck , that existence of a power series method which is stronger than multisummability would be equivalent to existence of an entire function with certain particular properties. We then prove that such entire functions cannot exist. In contrast to this negative result, we show that an iteration of power series methods is indeed stronger than multisummability.