Sur le développement en séries des fonctions implicites
The aim of this paper is to obtain a generalization of W. A. Woyczyński and B. Ram results concerning integrability of power series in terms of their coefficients for the class GM of general monotonic sequences.
We strengthen a result of Chui and Parnes and we prove that the set of universal Taylor series is a -dense subset of the space of holomorphic functions defined in the open unit disc. Our result provides the answer to a question stated by S.K. Pichorides concerning the limit set of Taylor series. Moreover, we study some properties of universal Taylor series and show, in particular, that they are trigonometric series in the sense of D. Menchoff.