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Periodic oscillations of coefficients of power series that satisfy functional equations, a practical revision (2302.12646v2)

Published 24 Feb 2023 in math.FA, math.CA, and math.CO

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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