Hello all you tetration brainies out there,

looking somewhat deeper into the intuitive Abel function of f(x)=b*x (which is supposed to be log_b(x) however unproven until now), I found a somewhat direct expression of the coefficients, which boils down to the following challenging question:

Let the sequence be defined recursively in the following way for :

and for

Is ?

Does it converge? The following graph of the sequence for , leaves the question open:

(The messed up numbers on the left side are due to a bug in sage *sigh*)

An equivalent slightly nicer formulation of the problem

Let the sequence be defined recursively in the following way for :

and for

Is ?

edit: this can be found now as TPID 9 in the open problems thread.

looking somewhat deeper into the intuitive Abel function of f(x)=b*x (which is supposed to be log_b(x) however unproven until now), I found a somewhat direct expression of the coefficients, which boils down to the following challenging question:

Let the sequence be defined recursively in the following way for :

and for

Is ?

Does it converge? The following graph of the sequence for , leaves the question open:

(The messed up numbers on the left side are due to a bug in sage *sigh*)

An equivalent slightly nicer formulation of the problem

Let the sequence be defined recursively in the following way for :

and for

Is ?

edit: this can be found now as TPID 9 in the open problems thread.