Cyclic Functions under Differentiation
This Demonstration explores functions (such as sine and cosine) that are cyclic under differentiation with period four. Such a function is uniquely determined by its value and first three derivatives at a point. The thick curve is the cyclic function itself, and the dotted curves are the first four truncations of its Maclaurin series.
An cyclic function is defined as a solution of .
This is an explicit form for a fourth cyclic function: