Periodic oscillations of coefficients of power series that satisfy functional equations, a practical revision

Abstract

For the solutions $\Phi (z)$ of functional equations $\Phi (z)=P(z)+\Phi (Q(z))$, we derive a complete asymptotic of power series coefficients. As an application, we improve significantly an asymptotic of the number of $2,3$-trees with $n$ leaves given in Adv. Math. 44:180-205, 1982 by Andrew M. Odlyzko. The methods we consider can be applied to more general functional equations too.

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