Lemniscate elliptic functions: Difference between revisions

Content deleted Content added

Revision as of 01:50, 18 August 2025 edit Jacobolus (talk \| contribs) Extended confirmed users 40,094 edits m Undid revision 1306495131 by 192.52.240.206 (talk) – the specific whitespace style is largely irrelevant, but changes like this add pointless watchlist spam and make it difficult to compare different versions of the article. If you write new articles from scratch or undertake a major rewrite, feel free to set up the whitespace to your own preference. but don't make further changes like this elsewher Tag: Undo ← Previous edit		Latest revision as of 18:12, 18 August 2025 edit undo Jacobolus (talk \| contribs) Extended confirmed users 40,094 edits m →Relation to the modular lambda function
(4 intermediate revisions by 2 users not shown)
Line 711: &\quad {}= \frac 2 {2 + \sqrt{7} + \sqrt{21 + 8 \sqrt{7}} + \sqrt{2 {14 + 6 \sqrt{7} + \sqrt{455 + 172 \sqrt{7}}}}} \\[18mu] & {\operatorname{sl}}\bigl(\tfrac1{18}\varpi\bigr)\, {\operatorname{sl}}\bigl(\tfrac3{18}\varpi\bigr)\,{\operatorname{sl}}\bigl(\tfrac5{18}\varpi\bigr)\,{\operatorname{sl}}\bigl(\tfrac7{18}\varpi\bigr) \\~~[-3mu]~~ &\quad {}= \sqrt[8]{\frac{\lambda (9i)}{1-\lambda (9i)}} = {\tan}\~~Biggl~~left(\vphantom{\frac\Big\|\Big\|}\right. \frac\pi4 - {\arctan}\~~Biggl~~left(\vphantom{\frac\Big\|\Big\|}\right.\frac{2\sqrt[3]{2\sqrt{3}-2}-2\sqrt[3]{2-\sqrt{3}}+\sqrt{3}-1}{\sqrt[4]{12}}\~~Biggr~~left.\left.\vphantom{\frac\Big\|\Big\|}\right)\~~Biggr~~right) \end{aligned}</math>