Physical interpretation of the Pade approximation of the plasma dispersion function

It is shown that using Pade approximants in the evaluation of the plasma dispersion function Z for a Maxwellian plasma is equivalent to the exact treatment for a plasma described by a 'simple-pole distribution', i.e. a distribution function that is a sum of simple poles in the complex velocity plane (nu plane). In general, such a distribution function will have several zeros on the real nu axis, and negative values in some ranges of nu. This is shown to be true for the Pade approximant of Z commonly used in numerical packages such as WHAMP. The realization that an approximation of Z is equivalent to an approximation of f(nu) leads the way to the study of more general distribution functions, and we compare the distribution corresponding to the Pade approximant used in WHAMP with a strictly positive and monotonically decreasing approximation of a Maxwellian.