Finding the Simplest Polynomial for a Series

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The discussion focuses on finding the simplest polynomial for a series using a method related to Newton's divided difference formula. A participant shares a resource that explains this method in detail, noting that while their approach differs slightly, the core principles are similar. The conversation highlights the importance of understanding why the method works, referencing Newton's polynomial for further clarity. The shared links provide additional context and resources for those interested in the mathematical foundations. Overall, the thread emphasizes the utility of established formulas in simplifying polynomial expressions for series.
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I cannot for the life of me remember where I learned to do this nor can I remember why this works, but I know a method for finding the simplest polynomial for a series. I had something half typed up and then I found this site: http://www.johansens.us/sane/technotes/formula.htm which explains a method more thoroughly. While this is not identical to the way I do it, it is certainly similar enough.

So why does this work?
 
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