Generating asymptotics for factorially divergent sequences

Understand

The algebraic properties of formal power series, whose coefficients show factorial growth and admit a certain well-behaved asymptotic expansion, are discussed.

• It is shown that these series form a subring of $\mathbb{R}[[x]]$.
• This subring is also closed under composition and inversion of power series.
• An 'asymptotic derivation' is defined which maps a power series to the asymptotic expansion of its coefficients.