05/12/2009, 08:54 AM

(05/11/2009, 12:55 PM)sheldonison Wrote: Are and the same two functions in the Bummer post?Yes. These are the same functions.

Henryk asked me to plot them all versus real argument as a separate post.

(05/11/2009, 12:55 PM)sheldonison Wrote: Could you comment on how the behavior of the two functions differ in the complex plane?Yes.

Functions and entire.

One of them can be obtained from another one, just displacing the argument.

Tetration has, as you know, singularities and the cutline; due to the periodicity, there is set of singulatities and cutlines. Function can be obtained by translation of tetration , so, it has similar singulatities.

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(05/11/2009, 12:55 PM)sheldonison Wrote: Do both functions have the same values at z=+/-i*infinity?No. There is no need to talk about values ,

because each of them is periodic and the periods are imaginary.

(05/11/2009, 12:55 PM)sheldonison Wrote: Do they have the same periodicity?No. Periods are different:

(05/11/2009, 12:55 PM)sheldonison Wrote: Does only one have singularities?Tetration has singularities;

its displacement has too.

(05/11/2009, 12:55 PM)sheldonison Wrote: Given that at all integer values of z, then can these two functions be expressed in terms of each other, where ?Yes.

(05/11/2009, 12:55 PM)sheldonison Wrote: Is the function analytic?Yes.

is 1-periodic function; it is almost sinusoidal.

Henryk, can we begin to distribute the draft of our paper?

It would answer a lot of questions we provoked with the plot...