Evaluate numerically:

Evaluate to high precision:

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

Evaluate efficiently at high precision:

HeavisideLambda threads over lists:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix HeavisideLambda function using MatrixFunction:

Values of HeavisideLambda at fixed points:

Value at zero:

Evaluate symbolically:

Find a value of x for which the HeavisideLambda[x]=0.6:

Plot the HeavisideLambda function:

Visualize scaled HeavisideLambda functions:

Visualize the composition of HeavisideLambda with a periodic function:

Plot HeavisideLambda in three dimensions:

Function domain of HeavisideLambda:

It is restricted to real inputs:

Function range of HeavisideLambda:

HeavisideLambda is an even function:

The area of HeavisideLambda is 1:

HeavisideLambda has singularities:

However, it is continuous everywhere:

Verify the claim at one of its singular points:

HeavisideLambda is neither nonincreasing nor nondecreasing:

HeavisideLambda is not injective:

HeavisideLambda is not surjective:

HeavisideLambda is non-negative:

HeavisideLambda is neither convex nor concave:

TraditionalForm typesetting:

Differentiate the univariate HeavisideLambda:

Higher derivatives with respect to x:

Differentiate the multivariate HeavisideLambda:

Differentiate a composition involving HeavisideLambda:

Integrate over finite domains:

Integrate over infinite domains:

Numerical integration:

Integrate expressions containing symbolic derivatives of HeavisideLambda:

FourierTransform of HeavisideLambda is a squared Sinc function:

FourierSeries:

Find the LaplaceTransform of HeavisideLambda:

The convolution of HeavisideLambda with HeavisidePi: