Modular lambda function: Difference between revisions

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Revision as of 11:20, 18 April 2021

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These are the relations between lambda-star and the Ramanujan-G-function:

:<math>G(x) = \sin[\{2\arcsin[\lambda^*(x)]]\}^{-1/12} = 1/[\sqrt[12]{2\lambda^*(x)}\sqrt[24]{1-\lambda^*(x)^2}] </math>

:<math>g(x) = \tan[\{2\arctan[\lambda^*(x)]]\}^{-1/12} = \sqrt[12]{[1-\lambda^*(x)^2]/[2\lambda^*(x)]} </math>

:<math>\lambda^*(x) = \tan[\{ \frac{1}{2}\arctan[g(x)^{-12}]]\} = \sqrt{g(x)^{24}+1}-g(x)^{12} </math>

===Special Values===