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Sharp double inequality for complete elliptic integral of the first kind
- Publication Year :
- 2021
-
Abstract
- For $r\in(0,1)$, the function $\K(r)=\int_0^{\pi/2}(1-r^2\sin^2t)^{-1/2}dt$ is known as the complete elliptic integral of the first kind. In this paper, we prove the absolute monotonicity of two functions involving $\K(r)$. As a consequence, we improve Alzer and Richards' result.
- Subjects :
- Mathematics - Classical Analysis and ODEs
33E05, 33C75
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2104.11630
- Document Type :
- Working Paper