Piece-wise power-law fits to the HI, HeI, and HeII photo-ionisation cross-section (top panels) and the associated relative error (lower panels). The black dotted line shows the cross-sections from Verner et al. (1996), the blue dashed lines a simple power-law fit, and the red solid lines a power-law series (Eq. 5). The horizontal dotted lines in the lower panels indicate relative errors of 1% and 10%.