The plasma dispersion function and its numerical calculation

The plasma dispersion function (PDF) is widely used in plasma physics, especially for the interaction between waves and plasmas. It is essentially important to quickly and precisely calculate the values of the PDF and its differentials with any orders. Related efforts have been ongoing from the beginning when this function is proposed until recent decades, where lots of brilliant ideas bore and some behave well in specific situations. The paper aims to review different calculation methods of the PDF and its differentials, especially to compare their properties in numerical calculations, including calculation accuracy, calculation speed, and storage requirements. Then some appropriate optimization numerical calculation methods can be recommended in different application scenarios.