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We analyze the mathematical structure of equations for temperature Tc of thesuperconductivity transition in a gas of interacting Fermi particles or at thephonon-mediated pairing in a metal in case of non-adiabatic conditions, i. e.,when the characteristic phonon frequency is comparable or larger than the Fermienergy . The integral equations for Tc are derived in the logarithmicalapproximation. The equations contain no divergent terms in the anti-adiabaticlimit.

Notes on calculating temperature of the superconducting transition: interacting fermi gas and phonon mechanisms in non-adiabatic regime