We calculate and plot the synchrotron power, Pν, the absorption coefficient, αν, and the source function, Sν, for a power-law distribution of charged particles with Lorentz parameter values γ1 ⩽ γ ⩽ γ2. For this purpose, we define parametric functions Zp(x, η), Hp(x, η), and Yp(x, η) with η = γ2/γ1, such that Pν ∝ Zp(γ−21ν/ν0, η), αν ∝ Hp(γ−21ν/ν0, η), and Sν ∝ Yp(γ−21ν/ν0, η). Corresponding asymptotic forms are also calculated and plotted for three frequency ranges, i.e., x ≪ 1, 1 ≪ x ≪ η2, and x ≫ η2, especially in the case of finite parameter η. Asymptotic forms of the middle range are possible for functions Zp and Yp for p>1/3, and for function Hp for all positive values of index p. A characteristic value, ηc(p, ε) (with ε ≪ 1), is then defined for each of the above functions so that for η ≳ ηc(p, ε) the middle range asymptotic forms could be considered. Further calculation details are also presented and discussed.