Modular lambda function: Difference between revisions

Revision as of 08:25, 19 April 2021

Revision as of 08:26, 19 April 2021

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

:<math>\lambda^*(x) = |k| </math>

The values of λ*(x) can be computed as follows: