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 computing the error function in the multiple regions of the complex plane. The text also elaborates on the general behavior of the functions. The book is a dependable reference for readers interested in the plasma dispersion function.