Cyclic Functions under Differentiation
Initializing live version
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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
An cyclic function is defined as a solution of .
This is an explicit form for a fourth cyclic function: