The exact plasma dispersion functions in the complex region

Abstract

The exact relativistic plasma dispersion functions are continued analytically into the complex plane, on the basis of a general method derived from the theory of singular Cauchy-type integrals. The main analytic properties of the dispersion functions in the complex region are studied and the physical consequences and applications of this method for ITER conditions are discussed.

Analytical Evaluation of the Plasma Dispersion Function Using Binomial Coefficients and Incomplete Gamma Functions

“…In the literature, various efficient numerical methods have been proposed for improving the evaluation of the PD function [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Due to the fact that the PD function can not be directly expressed in a closed form, many approximations for the (PD) function have been proposed.…”