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Monotonicity rules for the ratio of power series

Published 28 Apr 2024 in math.CA | (2404.18168v1)

Abstract: In this paper, we present some monotonicity rules for the ratio of two power series $x\mapsto \sum_{k=0}\infty a_k xk / \sum_{k=0}\infty b_k xk$ 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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Authors (2)

  1. Zhong-Xuan Mao 
  2. Jing-Feng Tian 

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