ANALYTICAL SOLUTION OF THE NON-DISCRETIZED RADIATIVE-TRANSFER EQUATION FOR A SLAB OF FINITE OPTICAL DEPTH

An analytical solution of the radiative transfer equation for a plane parallel slab of finite depth is presented without requiring discretiz ation in space or angles. The solution, expressed in terms of the matr ix hyperbolic tangent function, avoids the problem of exponentially in creasing terms so that it is also suitable for numerical calculations. By using the resolvent of the transfer equation we obtain simple seri es expansions for the matrix elements.