On approximating the arc lemniscate functions

This paper deals with the arc lemniscate functions from the point view of bivariate means which have been introduced in [ 1 ]. In this study, several optimal bounds for these bivariate means in terms of arithmetic, geometric and quadratic means are established. As a consequence, new bounds for the a...

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Bibliographic Details
Published inIndian journal of pure and applied mathematics Vol. 53; no. 2; pp. 316 - 329
Main Authors Zhao, Tie-Hong, Qian, Wei-Mao, Chu, Yu-Ming
Format Journal Article
LanguageEnglish
Published New Delhi Indian National Science Academy 2022
Springer Nature B.V
Subjects
Applications of Mathematics
Bivariate analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
Lemniscate mean
Gauss’ arc lemniscate functions
33E05
Bivariate means
26D07
Inequalities
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Summary:This paper deals with the arc lemniscate functions from the point view of bivariate means which have been introduced in [ 1 ]. In this study, several optimal bounds for these bivariate means in terms of arithmetic, geometric and quadratic means are established. As a consequence, new bounds for the arc lemniscate functions are also derived, which improve some previously known results.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-021-00016-9