In this paper, we present some monotonicity rules for the ratio of two power series x↦ ∑ₖ₌₀^∞ aₖ xᵏ / ∑ₖ₌₀^∞ bₖ xᵏ under the assumption that the monotonicity of the sequence aₖ/bₖ changes twice. Additionally, we introduce a local monotonicity rule in this paper.
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Mao et al. (2024) studied this question.
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