fibonacci like

[tommy1729]

Periodic ones exist; indeed all the "basis" solutions \( e^{uz} \) are periodic with complex period \( \frac{2\pi i}{u} \).

maybe there are solutions with other periods as well.

playing around with the c_n coefficients we can construct another periodic solution i guess.

i conjectured about non-periodic entire functions only , because it might be that there exist periodic solutions that are of a different form ?

i was aware of the period of the "basis" solutions , i just didnt express myself very well.

you are correct of course.

i hope nobody minds this is not really about tetration.

( and apparantly recursion is reserved for the integers as bo explained )