Absolute value |ℰ_F| of the relative difference between the exact and approximate flux calculation in a bin, Eq. (7), as a function of the flux spectral index α. Two mean rigidity definitions are compared, in dim grey and in light grey, see Eq. (5), for different bin size ranges (from 1 decade, solid line, down to 0.1 decade, dotted line). To guide the eye, the green dash-dotted line shows when the relative difference is 3%. See text for discussion.