The recently developed proximity effect theory of Takahashi and Tachiki is shown to be equivalent to another formulation, which starts from Usadel's dirty-limit version of the Eilenberger theory. The widely applied Werthamer approximation is obtained along new lines and is clearly shown to correspond to the thick layer limit. The thin layer limit for zero magnetic field reproduces the Cooper-de Gennes expression for the critical temperature T c, while a new and easily applicable expression is presented for the finite field case. The exact and limiting descriptions are illustrated by applications on Nb/Cu and Nb/Al multilayers, using bulk values for the density of states N, the pairing potential coupling constant V, and the diffusion constant D. Results are shown for T c as well as for the perpendicular and parallel upper critical fields H c2,⊥ and H c2,||. It appears that the diagonal approximation can underestimate the critical fields up to thirty percent. A new expression for the sum over the Matsubara frequencies, valid for all eigenvalues, is applied. It is shown that the new expression bridges the gap between the text book expression for small eigenvalues and the limiting expression for large eigenvalues used by Auvil and Ketterson.