On convergence of generalized power series that is the formal solution of algebraic ODE

In preprint of Keldysh Institute of Applied Mathematic of RAS (№ 65, 2013) Goryuchkina I. V. proposed the sketch of the proof of the theorem on sufficient condition of convergence near zero of generalized power series, that formally satisfies to algebraic (polynomial) ordinary differential equation. At that there considers the case that the set of power exponents of this generalized power series has only one nonrational generatrix. Here we give analytic proof of this theorem in details.