On the summability of a class of formal power series

Abstract

The formal power series solutions for some classes of moment differential equations, induced by polynomial moment differential operators, are characterized in terms of their summability properties, and in terms of estimates for recursive expressions involving their coefficients. Of special interest are the particularization of these results to classes of fractional and of ordinary differential equations. The Stokes’ phenomenon can be described in some of these situations. The main results are extended into the framework of q-Gevrey asymptotics and q-difference equations.