The Solution of the Fluctuation Problem in Electron-Photon Shower Theory

The analytical solution is given for the fluctuation problem arising in electron-photon shower theory under approximation $A$. The diffusion equations for two fundamental distribution functions are derived, and by transforming them into matrix recurrence relations their solution is obtained directly. From one of these distribution functions follows the analytical solution for the ($n,m$)th moments. The method of solution is similar to that previously employed by Messel and Potts to solve the fluctuation problems in nucleon shower theory. The $G$-equations used by Janossy and Scott play no role in the solution of the problem.