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Asymptotic limit for the thermodynamics of a boson-exchange superconductor.

We establish formulas for the free-energy difference (..delta..F) between the superconducting and normal states of an Eliashberg superconductor valid in the asymptotic limit lambda..-->..infinity where lambda is the mass-renormalization parameter. It is shown that (..delta..F) varies as lambda..omega../sub E//sup 2/ times a universal function of the reduced temperature t = T/T/sub c/. Here ..omega../sub E/ is the characteristic energy of the exchanged boson. The universal function is calculated numerically for finite t>0.