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arXiv · 2409.09809

Explicit Expressions for Iterates of Power Series

Kei Beauduin
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Abstract

In this paper, we present several formulas for both the discrete and fractional iterates of an invertible power series $f$, using a new unifying approach based on umbral calculus. Known formulas are extended, and their proofs simplified, while new expressions are introduced. In particular, by employing $q$-calculus identities, we eliminate the requirement for $f'(0)$ to equal $1$ and the resulting general expressions for the iterative logarithm are obtained as well.

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Kei Beauduin. 2025-12-04. Explicit Expressions for Iterates of Power Series. https://arxiv.org/abs/2409.09809

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