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arXiv · 2602.12494

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

Mario DeFranco
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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.

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Mario DeFranco. 2026-02-13. On recurrence relations arising from NRS(2) applied to a cubic polynomial. https://arxiv.org/abs/2602.12494

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