Estimated β_mn coefficients, b_n for an ionized gas with electron density of 10⁷ cm^-3, and electron temperature of 10 000 K. The solid red line shows the β_mn values derived by Walmsley (1990) for Hnα transitions, while the solid and dashed blue lines show the values derived by Storey & Hummer (1995) for Hnα and Hnβ transitions, respectively. The observed zig-zag for the β_mnStorey & Hummer (1995) coefficients for n > is due to the numerical error in deriving them from Eq. (8). This error increases for increasing n since the relative difference between the b_m and b_n decreases as observed in Fig. 1.