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A Series Expansion of a Logarithmic Expression and a Decreasing Property of the Ratio of Two Logarithmic Expressions Containing Sine

Author

Listed:
  • Xin-Le Liu

    (School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China)

  • Hai-Xia Long

    (School of Information Science and Technology, Hainan Normal University, Haikou 571158, China)

  • Feng Qi

    (School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China
    Independent Researcher, Dallas, TX 75252-8024, USA)

Abstract

In the paper, by virtue of a derivative formula for the ratio of two differentiable functions and with the help of a monotonicity rule, the authors expand a logarithmic expression involving the sine function into the Maclaurin power series in terms of specific determinants and prove a decreasing property of the ratio of two logarithmic expressions containing the sine function. These results are interesting purely in pure mathematics.

Suggested Citation

  • Xin-Le Liu & Hai-Xia Long & Feng Qi, 2023. "A Series Expansion of a Logarithmic Expression and a Decreasing Property of the Ratio of Two Logarithmic Expressions Containing Sine," Mathematics, MDPI, vol. 11(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3107-:d:1193945
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    Citations

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    Cited by:

    1. Feng Qi, 2024. "Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function," Mathematics, MDPI, vol. 12(18), pages 1-11, September.
    2. Da-Wei Niu & Feng Qi, 2024. "Monotonicity Results of Ratios between Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine," Mathematics, MDPI, vol. 12(12), pages 1-20, June.

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