Cyclic Functions under Differentiation

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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.

Contributed by: William Perry (March 2011)
Open content licensed under CC BY-NC-SA


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An cyclic function is defined as a solution of .

This is an explicit form for a fourth cyclic function:

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