New inequalities between the inverse hyperbolic tangent and the analogue for corresponding functions

In this paper, we present new inequalities which reveal further relationship for both the inverse tangent function arctan ( x ) and the inverse hyperbolic function arctanh ( x ) . At the same time, we give the analogue for inverse hyperbolic tangent and other corresponding functions.

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2020; no. 1; pp. 1 - 8
Main Authors Chen, Xiao-Diao, Nie, Long, Huang, Wangkang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 07.05.2020
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Hyperbolic functions
Inequalities
Inverse hyperbolic sine function
Inverse hyperbolic tangent function
Inverse sine function
Inverse tangent function
Mathematics
Mathematics and Statistics
Inverse tangent function
Inverse sine function
Inverse hyperbolic sine function
Inverse hyperbolic tangent function
Inequalities
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Summary:In this paper, we present new inequalities which reveal further relationship for both the inverse tangent function arctan ( x ) and the inverse hyperbolic function arctanh ( x ) . At the same time, we give the analogue for inverse hyperbolic tangent and other corresponding functions.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02396-8