Modular lambda function: Difference between revisions

Revision as of 08:26, 19 April 2021

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===Definition and computation of lambda-star===

The function λ*(x) gives the value of the elliptic modulus k, for which the complete [[elliptic integral]] of the first kind K(k) and its complementary counterpart K([sqrt(1-k^2))] are related by following expression:

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