Hm, this is strange. I just tried numerically the half iterate of and it looks quite convergent.

However I read in the article of Erdös and Jabotinsky [1]:

Now I am confused. If someone wants to compare, I computed the half iterate of to be

I verified that indeed and it converges for example for

Where is the mistake?

[1] P. Erdös and E. Jabotinksy, On analytic iteration, J. Analyse Math. 8, 1960/1961, 361-376.

[2] I. N. Baker, Zusammensetzungen ganzer Funktionen, Math. Z 69, 1958, 121-163.

[3] M. Levin, MSc. Thesis, Israel Institute of Technology, 1960.

However I read in the article of Erdös and Jabotinsky [1]:

Quote:The function was shown by I. N. Baker [2] to have no real non-integer iterates. M. Levine [3] showed, using some results of the present paper, that this function and the functions and have no analytic iterate.

Now I am confused. If someone wants to compare, I computed the half iterate of to be

I verified that indeed and it converges for example for

Code:

`1.0,1.250000000,1.270833333,1.270833333,1.271093750,1.271017795,1.271019345,1.271034749,1.271025674,1.271025591,1.271029198,1.271027503`

Where is the mistake?

[1] P. Erdös and E. Jabotinksy, On analytic iteration, J. Analyse Math. 8, 1960/1961, 361-376.

[2] I. N. Baker, Zusammensetzungen ganzer Funktionen, Math. Z 69, 1958, 121-163.

[3] M. Levin, MSc. Thesis, Israel Institute of Technology, 1960.