Monotonicity rules for the ratio of power series
Zhong-Xuan Mao, Jing-Feng Tian · arXiv (Cornell University) · 2024
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.