一个包含三角函数的函数的两个导数所定义的两个函数的完全单调性和单调性的充分必要条件

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2021-01-01 DOI:10.2298/aadm191111014q

Feng Qi (祁锋)

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引用次数: 7

摘要

本文利用拉普拉斯变换的卷积定理、完全单调函数的Bernstein定理、包含指数函数的函数的一些性质以及其他解析技术，得到了包含三角函数的函数的两个导数所定义的两个函数是完全单调或完全单调的充分必要条件。这些结果推广了相应的已知结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic. These results generalize corresponding known ones.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).