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math.CO2024
Explicit Expressions for Iterates of Power Series
Kei Beauduin
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.…
math.CO2024
Operational Umbral Calculus
Kei Beauduin
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a system…
math.CO2024
Old and new powerful tools for the normal ordering problem and noncommutative binomials
Kei Beauduin
In this paper, we derive formal general formulas for noncommutative exponentiation and the exponential function, while also revisiting an unrecognized, and yet powerful theorem. Th…