On recurrence relations arising from NRS(2) applied to a cubic polynomial

Mario DeFranco

paper

On recurrence relations arising from NRS(2) applied to a cubic polynomial

arXiv:2602.12494

Abstract

We prove that the leading coefficient of the "error" terms of NRS(2) applied to a cubic polynomial $f (z)$ with starting point $(- \frac{a _{1}}{a _{2}}, - \frac{a _{1}}{a _{2}})$ are positive-coefficient rational functions in the zeros of $f (z)$ . We express these terms as a sum over combinatorial objects which we call radius-value trees.