A first hires look at tetration \(\lambda = 1\) and \(b = e\)

[sheldonison]

@sheldonison So we can rebuild Kneser's method tetration using the beta method? In any case, the numerical approximation algorithm of the beta method seems to be much better.


@JmsNxn You missed super-root. The robustness of the beta method seems well suited for generating super-root.

Hey Ember,

Beta itself is a well behaved analytic function, but the resulting tetration function may not be.  The critical question for the Beta tetration function is when is it analytic.  Se this thread and subsequent posts concerning Beta tetration for base "e", that show that it is nowhere analytic, and the Taylor series does not converge.  Then in a sense the tetration base "e" function is only defined at the real axis, and then you can't "rebuild Kneser's tetration" from the beta method.

James and I are still actively investing base sqrt(2) now.