Monotonous two-parameter functions for asymptoticly approximating the inequalities involving the inverse tangent functions

In this paper, we present a family of two-parameter functions, which are used to asymptoticly approximating the inverse tangent function. It can recover some of previous results, and it can also recover the inverse tangent function itself. Numerical examples show that the new inequalities can achiev...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 116; no. 1
Main Authors Chen, Xiao-Diao, Qian, Cheng, Zhu, Ping, Pan, Xianghui
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2022
Springer Nature B.V
Subjects
Applications of Mathematics
Approximation
Asymptotic properties
Inequalities
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Parameters
Theoretical
Inverse tangent function
Secondary 33B10
Inequalities
Monotonous two-parameter function
Asymptotic approximation
Primary 26D05
26D15
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Summary:In this paper, we present a family of two-parameter functions, which are used to asymptoticly approximating the inverse tangent function. It can recover some of previous results, and it can also recover the inverse tangent function itself. Numerical examples show that the new inequalities can achieve much better approximation performance that those of prevailing methods.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-021-01152-x