On a Difference Equation Method in Cosmic-Ray Shower Theory

The recent results of Synder and Bhabha-Chakrabarty for the cascade theory of cosmic-ray showers are shown to be devirable from a general approach involving the use of the Laplace and Mellin transforms, and a general and powerful method, due to Synder, for solving the resulting difference equations. Boundary conditions are introduced in a natural and automatic way, and the accuracy of the solution is limited by the possible ways of evaluating the resulting triple complex integral.