Representing the lofgitudinal dielectric permittivity of relativistiс plasma by a convenience series in the long-wave region

For the longitudinal dielectric permittivity of relativistic plasma in the long-wave region, a representation in the form of a uniformly converging series is obtained; this representation is valid over a broad range of temperatures and wave vectors. If the temperature is not too small in the long-wave region, this series converges rapidly, ensuring high accuracy of the representation when only the first few terms of the series are used.