It involves defining a set of operators — like functors in CS, operators take one function and return another — which obey a modified form of the product rule f

It involves defining a set of operators — like functors in CS, operators take one function and return another — which obey a modified form of the product rule for derivatives D[f*g] = g*Df + f*Dg. These operators are used to make the analytic continuation of divergent series consistent; because they are defined in terms of functions that cannot be calculated directly from their definition (hence analytically continued), they are "alien".