The magnetoplasma dispersion function: some mathematical properties

The magnetoplasma dispersion function is defined as

It is found in all the dispersion relations for wave propagation perpendicular to the magnetic field in hot plasmas. We review the properties of f_ω(z), and present several new expansions, which may be of interest in the study of properties of waves in plasmas, or may suggest computational methods for calculating f_ω(z).