Specific heat difference functional derivative within strong coupling theory

A formal expression is derived for the functional derivative of the specific heat difference with respect to the electron-phonon spectral density valid for strong coupling superconductors and for all temperatures. A numerical solution of the Eliashberg equations is required to obtain results for the functional derivative. Moreover, a previous weak coupling approximation has been extended into the strong coupling regime and analytic expressions for the functional derivative atT_c have been derived. Finally, the way in which this work encompasses the previous weak coupling results is discussed.