The Polynomial Simplest Equations, the Symmetry Point, the Two Simplest Recurrence Equations, and the Method of Differences.

EasyChair Preprint 4423, version 3

Abstract

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 6^th 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.

Keyphrases: Method of finite differences, direction recurrence equation, general polynomial equation, general simplest equation, index direction, inflection point, offset study, polynomial inflection point, polynomials, recurrence equations, simplest equation

@booklet{EasyChair:4423,
  author    = {Charles Kusniec},
  title     = {The Polynomial Simplest Equations, the Symmetry Point, the Two Simplest Recurrence Equations, and the Method of Differences.},
  howpublished = {EasyChair Preprint 4423},
  year      = {EasyChair, 2023}}