Combinatorial Resolution of Systems of Differential Equations III: a Special Class of Differentially Algebraic Series

Abstract

We introduce and give a combinatorial model for a new class of formal power series: constructible differentially algebraic series. We show that this class is an algebra which is closed for inversion, substitution and inverse for substitution and study properties of their coefficients. We compare it to other families of series and give many examples and counter-examples (involving Euler, Bell, Stirling and Genocchi numbers).