Luke (1975, pp. 416–421) gives Chebyshev-series expansions for 𝐇n(x), 𝐋n(x), 0≤|x|≤8, and 𝐇n(x)−Yn(x), x≥8, for n=0,1; ∫0xt−m𝐇0(t)dt, ∫0xt−m𝐋0(t)dt, 0≤|x|≤8, m=0,1 and ∫0x(𝐇0(t)−Y0(t))dt, ∫x∞t−1(𝐇0(t)−Y0(t))dt, x≥8; the coefficients are to 20D.
MacLeod (1993) gives Chebyshev-series expansions for 𝐋0(x), 𝐋1(x), 0≤x≤16, and I0(x)−𝐋0(x), I1(x)−𝐋1(x), x≥16; the coefficients are to 20D.
Newman (1984) gives polynomial approximations for 𝐇n(x) for n=0,1, 0≤x≤3, and rational-fraction approximations for 𝐇n(x)−Yn(x) for n=0,1, x≥3. The maximum errors do not exceed 1.2×10⁻⁸ for the former and 2.5×10⁻⁸ for the latter.