Sharp bounds for Gauss Lemniscate functions and Lemniscatic means
| Autor: | Wei-Mao Qian, Miao-Kun Wang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | AIMS Mathematics, Vol 6, Iss 7, Pp 7479-7493 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2021437?viewType=HTML |
| Popis: | For $ a, b > 0 $ with $ a\neq b $, the Gauss lemniscate mean $ \mathcal{LM}(a, b) $ is defined by $ \begin{equation*} \mathcal{LM}(a,b) = \left\{\begin{array}{lll} \frac{\sqrt{a^2-b^2}}{\left[{ {\rm{arcsl}}}\left(\sqrt[4]{1-b^2/a^2}\right)\right]^2}, \ &a>b,\\ \frac{\sqrt{b^2-a^2}}{\left[{ {\rm{arcslh}}}\left(\sqrt[4]{b^2/a^2-1}\right)\right]^2},\ &a |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|