The Polynomial Simplest Equations, the Symmetry Point, the Two Simplest Recurrence Equations, and the Method of Differences
Charles Kusniec · Zenodo (CERN European Organization for Nuclear Research) · 2023
This study shows some applications of “Shift, Symmetry and Asymmetry in Polynomial Sequences”[5] study. We show the simplest equations for all polynomials up to 6th degree, the symmetry point coordinates, as well as the two possible simplest recurrence equations for each polynomial. We will show how and why the method of differences works conclusively on polynomials, while in any other non-polynomial function the method of differences never ends in a constant. This is a work that shows how polynomials work. It serves as a reference for many future studies and proofs. As an example, at the end we show an application to solve an open problem. Finally, we make a useful summary to be used on a daily basis. Please note that this document is a preprint and has not yet been peer-reviewed. It is intended for discussion and feedback within the scientific community to refine the approaches and conclusions presented.