The Plasma Dispersion Function: The Hilbert Transform of the Gaussian focuses on the reactions, transformations, and calculations involved in plasma dispersion function. The book first offers information on the properties of Z, including symmetry properties, values for special arguments, power series, asymptotic expansion, and differential equation characterization. The text then ponders on the applications to plasma physics. Numerical calculations on the function of Z are presented. The manuscript takes a look at table generation and accuracy wherein various methods are proposed in computin.