Analytical treatment of resistive wake potentials in round pipes

An analytical form for the longitudinal and transverse resistive wake potentials of point-like charges moving parallel to the axis of a round pipe with frequency-independent walls conductivity is obtained. The short-range wake potentials are presented by uniformly convergent series. e frequency-dependent conductivity, the resonator term of the longitudinal monopole wake potential is presented in analytical form. The diffusion term of the potential is modified to simple integral form.