10/03/2021, 09:13 PM
I see no reasons why iterations of this type should not be possible with the same techniques we used for tetration and related ones.
I once started a thread here about the superfunction of exp(z)+z.
Notice exp(z)+z also has no FINITE fixpoint just like your z + Γ(z).
But exp(z) + z has a fixpoint at negative infinity.
On the other hand , exp(z) + z has no poles.
And exp(z) + z has a nice asymp to z.
So the situation is different.
One could also wonder about the generalization z + Γ(z,v) for various v.
In particular v = 1 for obvious reasons.
On the other hand Γ(z,1) does have zero's.
----
the infinite composition/functional equation :
f(s+1) = t(s) f(s) + Γ( t(s) f(s) )
- where t(s) is like with the gaussian method - should work , not ?
Interesting question, thank you.
regards
tommy1729
I once started a thread here about the superfunction of exp(z)+z.
Notice exp(z)+z also has no FINITE fixpoint just like your z + Γ(z).
But exp(z) + z has a fixpoint at negative infinity.
On the other hand , exp(z) + z has no poles.
And exp(z) + z has a nice asymp to z.
So the situation is different.
One could also wonder about the generalization z + Γ(z,v) for various v.
In particular v = 1 for obvious reasons.
On the other hand Γ(z,1) does have zero's.
----
the infinite composition/functional equation :
f(s+1) = t(s) f(s) + Γ( t(s) f(s) )
- where t(s) is like with the gaussian method - should work , not ?
Interesting question, thank you.
regards
tommy1729