English

Monotonicity rules for the ratio of power series

Classical Analysis and ODEs 2024-04-30 v1

Abstract

In this paper, we present some monotonicity rules for the ratio of two power series xk=0akxk/k=0bkxkx\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 ak/bk{a_k/b_k} changes twice. Additionally, we introduce a local monotonicity rule in this paper.

Keywords

Cite

@article{arxiv.2404.18168,
  title  = {Monotonicity rules for the ratio of power series},
  author = {Zhong-Xuan Mao and Jing-Feng Tian},
  journal= {arXiv preprint arXiv:2404.18168},
  year   = {2024}
}