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math.CO2025
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.CO2025
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…