S. R. Das Gupta

A new representation of theH-functions of radiative transfer

We obtain a new representation of ChandrasekharsH-functionsH(z) corresponding to the dispersion functionT(z) = |δrs−frs(z)|, [frs(z)] is of rank one.H(z) is obtained in the formAbstractWe obtain a new representation of ChandrasekharsH-functionsH(z) corresponding to the dispersion functionT(z) = |δrs−frs(z)|, [frs(z)] is of rank one.H(z) is obtained in the form

A note on theH-functions of transfer problems in multiplying media

H\left( z \right) = \left( {A_0 + A_1 z} \right)/\left( {K + z} \right) - \sum\limits_1^n {\int\limits_{E_r } {P_r (x) dx/(x + z),} }

A new technique for exact and unique solution of transfer equations in finite media

WherePrx(=ør(x)/H(x)) is continuous onErwhich are subsets of [0, 1].Ao,A1are determinable constants andK is the positive root ofT(z),ør(x) are known functions. From this formH(z) is then obtained in terms of a Fredholm type integral equation. This new form ofH(z) has proved to be very useful in solving coupled integral equations involvingX-,Y-functions of transport problems.Pr(x) can be replaced by approximating polynomials whose coefficients can be determined as functions of the moments of known functions; a closed form approximation ofH(z) to a sufficiently high degree of accuracy is then readily available by term integrations.

On transfer equation in a semi-infinite atmosphere with albedo ω>1

ChandrasekharsH-functionH(z) corresponding to the dispersion functionT(z)=|δ rs −frs(z)|, where [f rs (z)] is of rank 1, is obtained in terms of a Cauchy integral whose density functionQ(x,ω 1,ω 2,...) can be approximated by approximating polynomials (uniformly converging toQ(x)) having their coefficients expressed as known functions of the parametersω r s. A closed form approximation ofH(z) to a sufficiently high degree of accuracy is then readily available by term by term integration.

An exact solution of time-dependent equation of transfer of trapped radiation in a finite absorbing medium

Some useful results and remodelled representations ofH-functions corresponding to the dispersion function

Laser radiation in active amplifying media treated as a transport problem : transfer equation derived and exactly solved

T\left( z \right) = 1 - 2z^2 \sum\limits_1^n {\int_0^{\lambda r} {Y_r } \left( x \right){\text{d}}x/\left( {z^2 - x^2 } \right)}