Physical interpretation of the Pade approximation of the plasma dispersionfunction

It is shown that using Pade approximants in the evaluation of the plasma di spersion function Z for a Maxwellian plasma is equivalent to the exact trea tment for a plasma described by a 'simple-pole distribution', i.e. a distri bution function that is a sum of simple poles in the complex velocity plane (nu plane). In general, such a distribution function will have several zer os on the real nu axis, and negative values in some ranges of nu. This is s hown to be true for the Pade approximant of Z commonly used in numerical pa ckages such as WHAMP. The realization that an approximation of Z is equival ent to an approximation of f(nu) leads the way to the study of more general distribution functions, and we compare the distribution corresponding to t he Pade approximant used in WHAMP with a strictly positive and monotonicall y decreasing approximation of a Maxwellian.