In generalization of (the already solved) TPID 6 and following this thread of Andrew:

Does the sequence of interpolating polynomials of the points defined by pointwise converge to a function on (0,oo) (, satisfying )?

If it converges:

a) is then the limit function analytic, particularly at the point ?

b) For let b[4]x be the regular superexponential at the lower fixpoint. Is then f(x)[4]x = x for non-integer x with ?

c) For let b[4]x be the super-exponential via Kneser/perturbed Fatou coordinates. Is then f(x)[4]x = x for non-integer x with ?

To be more precise we can explicitely give the interpolating polynomials:

,

the question of this post is whether

exists for each .

Does the sequence of interpolating polynomials of the points defined by pointwise converge to a function on (0,oo) (, satisfying )?

If it converges:

a) is then the limit function analytic, particularly at the point ?

b) For let b[4]x be the regular superexponential at the lower fixpoint. Is then f(x)[4]x = x for non-integer x with ?

c) For let b[4]x be the super-exponential via Kneser/perturbed Fatou coordinates. Is then f(x)[4]x = x for non-integer x with ?

To be more precise we can explicitely give the interpolating polynomials:

,

the question of this post is whether

exists for each .