Hello tetration freaks !
Karlin and Mcgregor showed that:
If
is a function holomorphic and single valued on the complement of a closed countable set in the extended complex plane. Let 
two fixed points of such that |,|f'(s_1)|\neq 0,1)
and \subseteq [s_1,s_2])
. Then the regular iterations at 
and 
are equal if and only if is a fractional linear function.
[1] Karlin, S., & Mcgregor, J. ( 1968 ). Embedding iterates of analytic functions with two fixed points into continuous groups. Trans. Am. Math. Soc., 132, 137–145.
However if is not true , can we have regular iterations that are independant of the fixpoint used ?
regards
tommy1729
Karlin and Mcgregor showed that:
If
[1] Karlin, S., & Mcgregor, J. ( 1968 ). Embedding iterates of analytic functions with two fixed points into continuous groups. Trans. Am. Math. Soc., 132, 137–145.
However if
regards
tommy1729