New Sharp Double Inequality of Becker–Stark Type

Zhu, Ling

doi:10.3390/math10040558

Mathematics

2022

DOI: 10.3390/math10040558

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New Sharp Double Inequality of Becker–Stark Type

Ling Zhu

Abstract: In this paper, we establish new sharp double inequality of Becker–Stark type by using a role of the monotonicity criterion for the quotient of power series and the estimation of the ratio of two adjacent even-indexed Bernoulli numbers. The inequality results are better than those in the existing literature.

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2024

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New refinements of Becker-Stark inequality

Wang,

Zhao

2024

MATH

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<abstract>This paper deals with the well-known Becker-Stark inequality. By using variable replacement from the viewpoint of hypergeometric functions, we provide a new and general refinement of Becker-Stark inequality. As a particular case, the double inequality <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \frac{\pi^2-(\pi^2-8)\sin^2x}{\pi^2-4x^2}<\frac{\tan x}{x}<\frac{\pi^2-(4-\pi^2/3)\sin^2x}{\pi^2-4x^2} \end{equation*} $\end{document} </tex-math></disp-formula> for $ x\in(0, \pi/2) $ will be established. The importance of our result is not only to provide some refinements preserving the structure of Becker-Stark inequality but also that the method can be extended to the case of generalized trigonometric functions.</abstract>

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New refinements of Becker-Stark inequality

Wang,

Zhao

2024

MATH

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New Sharp Double Inequality of Becker–Stark Type

Cited by 1 publication

References 12 publications

New refinements of Becker-Stark inequality

New refinements of Becker-Stark inequality

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