We consider questions relating to the convergence of generalized power series (with complex-valued exponents) that formally satisfy some analytic functional equations: a differential equation, a q-difference one, or a Mahler equation. We present new results, as well as generalizations of some of our previous results, thus summing up our investigations of the subject. We also present a selection of results on the existence and uniqueness of local holomorphic solutions of such equations and review some classical results on the convergence of Taylor power series that solve them formally. Bibliography: 54 titles.
Gontsov et al. (Wed,) studied this question.