Power series methods and multisummability

We recall the notion of a power series summability method and show, using r esults of W. BALSER and A. BECK, that existence of a power series method wh ich is stronger than multisummability would be equivalent to existence of a n entire function with certain particular properties. We then prove that su ch entire functions cannot exist. In contrast to this negative result, we s how that an iteration of power series methods is indeed stronger than multi summability.