Explicit Expressions for Iterates of Power Series
Combinatorics
2025-12-05 v3 Classical Analysis and ODEs
Abstract
In this paper, we present several formulas for both the discrete and fractional iterates of an invertible power series , 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 -calculus identities, we eliminate the requirement for to equal and the resulting general expressions for the iterative logarithm are obtained as well.
Cite
@article{arxiv.2409.09809,
title = {Explicit Expressions for Iterates of Power Series},
author = {Kei Beauduin},
journal= {arXiv preprint arXiv:2409.09809},
year = {2025}
}
Comments
16 pages, to be published