TheH-functions of radiative transfer in an active amplifying medium

We obtain two explicit closed form representations of Chandrasekhar'sH-functionsH(z) characterising transfer of radiation in an active amplifying medium corresponding to the dispersion function $$T(z) = 1 - 2z^2 intlimits_0^1 {Y(x)dx/(z^2 - x^2 ), Y(x)< 0 on [0, 1]} .$$ Their basic properties are derived and the values of theH-functionH(z, ω) whenY(x)=ω/2, are approximately computed for values of ω in the range (?10^?12)–(?10²) and for values ofzε[0, 1].