Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

KleinInvariantJ can be used with CenteredInterval objects:

Compute average-case statistical intervals using Around:

Values at fixed points:

Find the first positive maximum of the real part of KleinInvariantJ:

Plot the real part of KleinInvariantJ:

Plot the real part of J(τ) function:

Plot the imaginary part of J(τ) function:

Complex domain of KleinInvariantJ:

KleinInvariantJ is a periodic function:

KleinInvariantJ threads elementwise over lists:

KleinInvariantJ is an analytic function on its domain of definition:

It has no singularities or discontinuities there:

is neither nondecreasing nor nonincreasing:

KleinInvariantJ is not injective over the complexes:

is not surjective:

is neither non-negative nor non-positive:

is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to τ:

The first and second derivatives with respect to τ:

Plot the first and second derivatives with respect to τ:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Taylor expansion at a generic point: