Explicit Expressions for Iterates of Power Series
| Autor: | Kei, Beauduin |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we present five different formulas for both discrete and fractional iterations of an invertible power series $f$ utilizing a novel and unifying approach from umbral calculus. Established formulas are extended, and their proofs simplified, while new formulas are introduced. In particular, through the use of $q$-calculus identities, we eliminate the requirement for $f'(0)$ to equal $1$ and, consequently, the corresponding new expressions for the iterative logarithm are derived. Comment: 14 pages, to be published |
| Databáze: | arXiv |
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