Systematics at play in measuring j(< r). Left: sAM profile j(< r) normalized by the RF12 approximation (Eq. (3)) as a function of radius for disks with Sérsic n = 1 and a tanh rotation curve. The solid blue horizontal line represents the Eq. (3) approximation. The solid curves represent the sAM for various rotation curves with various turn-over radii R_t where the opacity of the line is inversely proportional to R_t/R_e. The vertical dotted line represents 2R_e. For galaxies with slowly rising rotation curves, with larger R_t, the RF12 approximation leads to a large overestimation of the total angular momentum (represented by the horizontal dashed lines), by 10–20%. Right: relative difference for the k_n coefficient between the k_n formula from RF12 and Eq. (4) as a function of Sérsic index n. One sees that Eq. (3) under- or over-estimate k_n by up to ∼10% for 0.5 < n < 4.