A modified asymptotic Padé method. Application to multipole approximation for the plasma dispersion function Z

Abstract

An improved asymptotic Padé method is presented. The approximations expressed as rational functions are developed both in a power series and asymptotic expansions. Identifying these developments with those for the exact function, the approximated rational functions are obtained. Three‐ and four‐pole approximations for the plasma dispersion function have been determined with this method. Our approximations (Z_lm) give closer results to the exact function than all the published ones.