New formulas for iteration

[Nolord]

Hello everyone,

I'm new to this forum  , I came across it during my research on fractional iteration!

I've derived, which are to my knowledge, new formulas for iteration of invertible power series via Umbral Calculus.

Here is the arxiv link.
I think that the main contribution is a the brevity of the proofs enabled by Umbral Calculus.

Please let me know your thoughts and I'll gladly answer any of your questions.

[MphLee]

Dear Nolord, thank you for your contribution. It seems very interesting. It actually sounds very exciting to me, but unfortunately, it falls into an area where I don't have much expertise. I'm sorry that this forum is currently a bit inactive, otherwise some users could have provided more constructive and targeted feedback.
In particular, your approach to the problem seems to be similar to Daniel's, and I'm sure it falls within JmsNxn's area of expertise. Why don't you try contacting him privately in case he doesn't see this thread?

Thank you again and welcome.