指数函数幂级数展开归一化尾部的绝对单调性

IF 2.3 3区数学 Q1 MATHEMATICS

Mathematics Pub Date : 2024-09-14 DOI:10.3390/math12182859

Feng Qi

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引用次数: 0

摘要

在这部著作中，作者回顾了无穷微分函数的麦克劳林幂级数展开的归一化尾部的起源，提出了指数函数的麦克劳林幂级数展开的两个归一化尾部之间的比值在正轴上是递减的，并证明了指数函数的麦克劳林幂级数展开的归一化尾部在整个实轴上是绝对单调的。

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

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.

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来源期刊

Mathematics Mathematics-General Mathematics

CiteScore

4.00

自引率

16.70%

发文量

4032

审稿时长

21.9 days

期刊介绍： Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.