The purpose of this paper is twofold. First, it is desired to show a new method of evaluating the coefficients that arise in the analysis of steady-state periodic operation of counterflow regenerators. The second purpose is to express the solution of the regenerator problem in terms of the functions F//n(u, v) and G//n(u, v) that permit, particularly with the new method of coefficient evaluation, a very rapid numerical description of regenerator operation. 8 Refs.