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

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