Infinite tetration giving I*Omega costant=I*0.567143...

[Ivars]

Ok that means \( \theta_{n+1}=\theta_n + A + B\sin(2\pi\theta_n) \) where \( A=\Omega \) and \( B=\frac{1}{4\Omega} \).

I put some effort into investigating this sequence \( \theta_n \). For the case of \( A \) and \( B \) that you describe one can see numerically that in the limit \( \theta_n = \alpha+n \) for some constant \( \alpha \).

Thanks,

It will .... take me some time to digest. I do not quite understand the first assumption,

one can see numerically that in the limit \( \theta_n = \alpha+n \) for some constant \( \alpha \).

As far as I did it (1850 terms), nothing is constant-You mean you replaced small difference of sin from -1 with an argument?
But as sin argument nears n*(3pi/2), can You do it?

As I see it since teta(n+1)-teta(n) = 1 when n-> infinity, there shall be no differences between teta(n) and n integer part.

There can not be one also in reals, since limit n->infinity is 1.

So this constant seems suspicious to me-or may be I misunderstood something.

Ivars