A new formulation and simplified derivation of the dispersion function for a plasma with a kappa velocity distribution

A simplified derivation of the relationship between the dispersion function for a plasma with a kappa velocity distribution and the Gauss hypergeometric function is presented. This derivation relies on only a few standard integrals. It naturally leads to a new integral representation for the dispersion function, which readily yields the power and Laurent series for it. The new integral representation is shown to be closely related to the Gordeyev integral for a kappa distribution.