On approximating the arc lemniscate functions

Tie-Hong Zhao (), Wei-Mao Qian () and Yu-Ming Chu ()
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Tie-Hong Zhao: Hangzhou Normal University
Wei-Mao Qian: Huzhou Vocational & Technical College
Yu-Ming Chu: Huzhou University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 316-329

Abstract: Abstract 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.

Keywords: Gauss’ arc lemniscate functions; Lemniscate mean; Bivariate means; Inequalities; 33E05; 26D07 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13226-021-00016-9

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