Weakly relativistic dielectric tensor and dispersion functions of a Maxwellian plasma

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Abstract
In order to study the absorption and emission properties of a magnetized plasma in the electron cyclotron range of frequencies, the weakly relativistic (Shkarofsky) plasma dispersion functions are simply and exactly expressed in terms of the Z function. This gives a useful working form to the dielectric tensor, for any wave vector and harmonic number, covering also the case of electron Maxwellian distributions drifting along the magnetic field.