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

Xin-Le Liu, Hai-Xia Long () and Feng Qi ()
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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

Mathematics, 2023, vol. 11, issue 14, 1-12

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.

Keywords: Maclaurin power series expansion; decreasing property; sine function; logarithmic expression; derivative formula; ratio of two differentiable functions; monotonicity rule (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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