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:
=\frac{1}{2\pi i}\int_{\gamma_L+\gamma_R+\gamma_T+\gamma_B} \frac{f(w)}{w-z} dw=\frac{1}{2\pi i}\int_{\gamma_V} -\frac{\log(f(w))}{w-1-z} + \frac{\exp(f(w))}{w+1-z}dw + \frac{1}{2\pi i}\int_{\gamma_H} -\frac{f(w)}{w+iA-z} + \frac{f(w)}{w-iA-z}dw<br />
)
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
In the version
But similarly we can compute the values on the horizontal line
So summarized we had the recursion formula:
Though the question is whether this is faster than the direct limit formula.