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Infinite tetration of the imaginary unit
#23
what if b^^0 is large ?

im not sure if we get the same behaviour.

if b^^0 is large we might reach divergence ?

or are we suppose to restrict b^^0 to the Shell-Thron region or their fixpoints ?

did anyone conjecture or prove bounds on b^^0 ?

i wonder how b = 1.71290 i , b^^0 = 1729 + 1729 i looks like.

the area within the cycles is also of interest.

perhaps not usefull , but i always try to map a cycle to a unit circle and then back again.

this can be done because of the riemann mapping theorem.

then i try to see how fast the iterations cycle on the unit circle ;

i (try to) study the complex angle theta of RIEMANN [superfunction(inversesuper(x_0) + n)] with respect to n.

( and this has the same period 2pi i / ln(ln(L)) ofcourse )

tommy1729
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Messages In This Thread
Infinite tetration of the imaginary unit - by GFR - 02/10/2008, 12:09 AM
RE: Infinite tetration of the imaginary unit - by tommy1729 - 06/20/2011, 10:22 PM

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