The H-functions of radiative transfer in an active amplifying medium (Q1058839)

We obtain two explicit closed form representations of Chandrasekhar's H- functions H(z) characterising transfer of radiation in an active amplifying medium corresponding to the dispersion function \[ T(z)=1- 2z^ 2\int^{1}_{0}Y(x)dx/(z^ 2-x^ 2),\quad Y(x)<0\quad on\quad [0,1]. \] Their basic properties are derived and the values of the H- function H(z,\(\omega)\) when \(Y(x)=\omega /2\), are approximately computed for values of \(\omega\) in the range \((-10^{-12})-(-10^ 2)\) and for values of \(z\in [0,1]\).