Modular lambda function: Difference between revisions

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:<math>\lambda^*(22) = (10-3\sqrt{11})(3\sqrt{11}-7\sqrt{2})</math>
 
:<math>\lambda^*(26) = (\sqrt{26}+5)(\sqrt{2}-1)^2\tan[\frac{\pi}{4}-\arctan(\frac{1}{3}\sqrt[3]{3\sqrt{3}+\sqrt{26}}-\frac{1}{3}\sqrt[3]{3\sqrt{3}-\sqrt{26}}+\frac{1}{6}\sqrt{26}-\frac{1}{2}\sqrt{2})]^4</math>
 
:<math>\lambda^*(30) = \tan\{\frac{1}{2}\arctan[(\sqrt{10}-3)^2(\sqrt{5}-2)^2]\}</math>
 
Lambda-star-values of integer numbers of 4n-1-type:
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:<math>\lambda^*(23) = \frac{1}{16\sqrt{2}}(5+\sqrt{23})[\frac{1}{6}(\sqrt{3}+1)\sqrt[3]{100-12\sqrt{69}}-\frac{1}{6}(\sqrt{3}-1)\sqrt[3]{100+12\sqrt{69}}+\frac{2}{3}]^4</math>
 
:<math>\lambda^*(27) = \frac{1}{16\sqrt{2}}(\sqrt{3}-1)^3[\frac{1}{3}\sqrt{3}(\sqrt[3]{4}-\sqrt[3]{2}+1)-\sqrt[3]{2}+1]^4</math>
 
Lambda-star-values of integer numbers of 4n-type:
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:<math>\lambda^*(4) = (\sqrt{2}-1)^2</math>
 
:<math>\lambda^*(8) = (\tan[\fracsqrt{12}+1-\sqrt{2}\arcsin(\sqrt{2}-1+2})]^2</math>
 
:<math>\lambda^*(12) = (\sqrt{3}-\sqrt{2})^2(\sqrt{2}-1)^2</math>
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:<math>\lambda^*(24) = \tan\{\frac{1}{2}\arcsin[(2-\sqrt{3})(\sqrt{3}-\sqrt{2})]\}^2</math>
 
:<math>\lambda^*(28) = (2\sqrt{2}-\sqrt{7})^2(\sqrt{2}-1)^4</math>
 
:<math>\lambda^*(32) = \tan\{\frac{1}{2}\arcsin[(\sqrt{2}+1-\sqrt{2\sqrt{2}+2})^2]\}^2</math>
 
Lambda-star-values of rational fractions: