Representation for a Plummer cluster (q, α)​ = ​(0, 0.25) of the cos I terms, D_cos​IF_rot (on the top left) and D_{cos​Icos​I}F_rot (on the top right), respectively with the first (on the bottom left) and second (on the bottom right) derivative with respect to cos I. In particular, the bottom right panel displays an approximate δ′(cos I) behaviour – the amplitude of the jumps tends to infinity as one reduces the step in the finite differentiation scheme – which is the expected theoretical relaxation induced by the sgn discontinuity of F_rot at t = 0.