Fast Computation of Some Asymptotic Functional Inverses

G. Robin showed that in several naturally occurring asymptotic expansions of the form , the polynomials Pn satisfy a simple relation P′n+1 = aP′n + (bn + c)Pn. These results do not give a way to compute these polynomials, since the constant term remains undetermined by this equation. In this note, we give a new derivation of some of Robinʹs results, and show how the constant terms can be computed with only manipulations of onevariable formal power series. From there, all the Pn can be computed efficiently.