Cite: 
[Xie2013] H. S. Xie, Generalized plasma dispersion function: One-solve-all treatment, visualizations, and application to Landau damping, Physics of Plasmas, 2013, 20, 092125, http://scitation.aip.org/content/aip/journal/pop/20/9/10.1063/1.4822332

% Hua-sheng XIE, huashengxie@gmail.com, IFTS-ZJU, 2013-05-26 23:37
% Calculate GPDF, Generalized Plasma Dispersion Function, see [Xie2013]
% Modify the parameters in the code for your own usage

Abstract
A unified, fast, and effective approach is developed for numerical
calculation of the well-known plasma dispersion function with
extensions from Maxwellian distribution to almost arbitrary
distribution functions, such as the $\delta$, flat top, triangular,
$\kappa$ or Lorentzian, slowing down, and incomplete Maxwellian
distributions. The singularity and analytic continuation problems
are also solved generally. Given that the usual conclusion
$\gamma\propto\partial f_0/\partial v$ is only a rough approximation
when discussing the distribution function effects on Landau damping,
this approach provides a useful tool for rigorous calculations of
the linear wave and instability properties of plasma for general
distribution functions. The results are also verified via a linear
initial value simulation approach. Intuitive visualizations of the
generalized plasma dispersion function are also provided.

Download: See supplementary material at http://dx.doi.org/10.1063/1.4822332 E-PHPAEN-20-024310 for the MATLAB version numerical routines, where GPDF, root finding, IVP simulation and test plotting codes are included. [ Supplementary Material]
ftp://ftp.aip.org/epaps/phys_plasmas/E-PHPAEN-20-024310

Also: http://arxiv.org/abs/1305.6476, http://arxiv.org/abs/1211.5984, http://arxiv.org/abs/1304.5883


Hua-sheng XIE (huashengxie@gmail.com, IFTS-ZJU)
14:22 2015/3/5