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

yes. They are also related to the earlier post which considers the two regular half iterates of on the interval (2,4), these are:

and

.

Quote:Could you comment on how the behavior of the two functions differ in the complex plane?

... Do they have the same periodicity?

... Does only one have singularities?

is entire, has period .

is not entire, has period .

Dmitrii can perhaps tell more about the singularities.

Quote: Do both functions have the same values at z=+/-i*infinity?They have no limit along the imaginary axis because they are imaginary periodic.

Quote:Given that at all integer values of z, then can these two functions be expressed in terms of each other, where ? Is the function analytic?

Yes, is analytic, though may somewhere have non-real singularities.