Chandrasekhar transformations improve convergence of computations of scattering from linearly stratified media

It is shown that repeated application of Chandrasekhar's transformation can extend the range of frequencies over which a classical perturbational solution of the one-dimensional Helmholtz equation converges, when the refractive index differs from unity within a fixed finite interval. A conjecture (supported by a computational example) is made that, for a given form for the refractive index, there is a particular number of Chandrasekhar transformations which optimizes the range of convergence. The computational significance of the results is discussed.