The monotonicity of ratios involving arc tangent function with applications

In this paper, we investigate the monotonicity of the functions on (0, ∞) for > 0, which not only gives relative errors of known bounds with quadratic for arctan , but also yields some new accurate bounds. Moreover, the known bounds are extended and a more accurate estimate for arctan is presente...

Full description

Saved in:
Bibliographic Details
Published inOpen mathematics (Warsaw, Poland) Vol. 17; no. 1; pp. 1450 - 1467
Main Authors Yang, Zhen-Hang, Tin, King-Fung, Gao, Qin
Format Journal Article
LanguageEnglish
Published Warsaw De Gruyter 01.01.2019
De Gruyter Poland
Subjects
absolute error
arctangent function
Primary 33B10
relative error
Secondary 26D05
sharp bounds
Online AccessGet full text
ISSN2391-5455
2391-5455
DOI10.1515/math-2019-0098

Cover

More Information
Summary:In this paper, we investigate the monotonicity of the functions on (0, ∞) for > 0, which not only gives relative errors of known bounds with quadratic for arctan , but also yields some new accurate bounds. Moreover, the known bounds are extended and a more accurate estimate for arctan is presented.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2019-0098