Iteration series

[bo198214]

The formula for the binomial-method, (which Henryk announced to the forum last year, was shown by Woon, and earlier by Comtet who credits again earlier use by Jabotinsky) is

Woon used linear operators he doesnt talk about functions.
Jabotinsky (and also Comtet I guess) derived a similar (finite) formula for power series with \( f_0=0 \), \( f_1=1 \).

The whole concept is then much more easier to read (and write) if we introduce an "umbral"-like notation, adapted to iteration-series.

Yes, its kinda umbral because generally \( (f+\text{id})^{\circ n}\neq \sum_{m=0}^n \left(n\\m\right) f^{\circ n} \).