06/10/2021, 12:21 PM

Hi, I know this is not directly related to tetration. It is related to iteration theory and solving functional equations.

https://math.stackexchange.com/questions...alpha-beta

The question is the following

Mind that here x,y can be thought to be numbers. But the crucial part is that , and are intended to be matrices, formal powerseries or functions (non commutative objects in general) under composition.

I ask also here because with JmsNxn deep familiarity with iterated composition (in the question i rendered the Omega notation as a product to not scare away normies) I could get some knowledge.

https://math.stackexchange.com/questions...alpha-beta

The question is the following

Mind that here x,y can be thought to be numbers. But the crucial part is that , and are intended to be matrices, formal powerseries or functions (non commutative objects in general) under composition.

I ask also here because with JmsNxn deep familiarity with iterated composition (in the question i rendered the Omega notation as a product to not scare away normies) I could get some knowledge.

MSE MphLee

Mother Law \((\sigma+1)0=\sigma (\sigma+1)\)

S Law \(\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)\)