Hi Dmitrii,

why not apply a similar Cauchy-integral technique for bases ?

Instead of letting the parameter go to infinity, we just choose to be the period of the tetration, i.e.

where .

In the version you compute the values of along the vertical line and compute the values to the left via and to the right on via .

But similarly we can compute the values on the horizontal line and conclude the values on the top line and on the bottom line equal to the values on via periodicity.

So summarized we had the recursion formula:

Though the question is whether this is faster than the direct limit formula.

why not apply a similar Cauchy-integral technique for bases ?

Instead of letting the parameter go to infinity, we just choose to be the period of the tetration, i.e.

where .

In the version you compute the values of along the vertical line and compute the values to the left via and to the right on via .

But similarly we can compute the values on the horizontal line and conclude the values on the top line and on the bottom line equal to the values on via periodicity.

So summarized we had the recursion formula:

Though the question is whether this is faster than the direct limit formula.