Explicit Expressions for Iterates of Power Series
arXiv:2409.09809
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.
16 pages, to be published