Approximations to inverse tangent function

In this paper, we present a sharp Shafer-type inequality for the inverse tangent function. Based on the Padé approximation method, we give approximations to the inverse tangent function. Based on the obtained result, we establish new bounds for arctan x .

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Bibliographic Details
Published in:Journal of inequalities and applications 2018, Vol.2018 (1), p.1-14, Article 141
Main Authors: Qiao, Quan-Xi, Chen, Chao-Ping
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Approximation
Inequality
Inverse trigonometric function
Mathematics
Mathematics and Statistics
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Description
Summary:In this paper, we present a sharp Shafer-type inequality for the inverse tangent function. Based on the Padé approximation method, we give approximations to the inverse tangent function. Based on the obtained result, we establish new bounds for arctan x .
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1734-7