lambda function

Lambda modular function

Evaluation of the lambda modular function.

lambda(tau, transfo = FALSE)

Arguments

• tau: a complex number with strictly positive imaginary part, or a vector or matrix of such complex numbers; missing values allowed
• transfo: Boolean, whether to use a transformation of the values of tau close to the real line; using this option can fix some failures of the computation (at the cost of speed), e.g. when the algorithm reaches the maximal number of iterations

Returns

A complex number, vector or matrix.

Note

The lambda function is the square of the elliptic modulus.

Examples

x <- 2
lambda(1i*sqrt(x)) + lambda(1i*sqrt(1/x)) # should be one