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Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function

Author

Listed:
  • Feng Qi

    (School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China
    School of Mathematics and Physics, Hulunbuir University, Hulunbuir 021008, China
    Independent Researcher, University Village, Dallas, TX 75252-8024, USA)

Abstract

In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis.

Suggested Citation

  • Feng Qi, 2024. "Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function," Mathematics, MDPI, vol. 12(18), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2859-:d:1478204
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    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

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    1. 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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