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arXiv · 2404.18168

Monotonicity rules for the ratio of power series

Zhong-Xuan Mao·Jing-Feng Tian
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Abstract

In this paper, we present some monotonicity rules for the ratio of two power series $x\mapsto \sum_{k=0}^\infty a_k x^k / \sum_{k=0}^\infty b_k x^k$ under the assumption that the monotonicity of the sequence ${a_k/b_k}$ changes twice. Additionally, we introduce a local monotonicity rule in this paper.

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Zhong-Xuan Mao, Jing-Feng Tian. 2024-04-28. Monotonicity rules for the ratio of power series. https://arxiv.org/abs/2404.18168

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