GENERALIZED PLASMA DISPERSION FUNCTIONS

Generalized plasma dispersion functions have recently arisen in the de rivation of an exact expression for the quadratic response tensor for a plasma with constituent species having Maxwellian velocity distribut ions. A range of mathematical properties satisfied by the generalized plasma dispersion functions are derived here, including recursion rela tions, series expansions, and approximate analytic forms, including Pa de approximants. These properties are of central importance to the app lication of the exact quadratic response tensor to descriptions of sec ond-order processes in weak and strong turbulence theory, such as thre e-wave interactions in warm plasmas. (C) 1998 American Institute of Ph ysics. [S0022-2488(98)02807-2].