A method for parametrization and expansion of distribution functions is presented. The expansion has a finite number of simple poles, which gives efficient numerical calculations and control of all converging moments. The low velocity region is Maxwell-like and the high-velocity tail follows an inverse power law. The method is applied to Maxwell-like distributions with and without suppressed tails. Dispersion relations can be obtained for a wide class of distributions, using building blocks available in any numerical library. Dispersion relations, for ordinary Langmuir waves and for beam-plasma interactions with intermediate temperature and beam to plasma density ratio, are derived. The Landau damping, obtained in the long wavelength regime, is of the same order but smaller than for the generalized Lorentzian distributions, for a given degree in the power law.

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