Recall in the post The Calculus Tree we had defined
Definition 3. A function is cyclic if for some nonzero finite number The number is called the differential order of and is denoted If a function is not cyclic we say (note in this definition ).
I said it followed that if was cyclic, then for some This was not justified (correspondingly I have fixed the arrows). Rather, the condition is certainly sufficient for to be cyclic.
So real cyclic functions must have the form no more complicated than
where and for all and some
For example is cyclic (of differential order 4) with and yielding