The structure of the equation of state $omega$ could be very complicate in nature while a few linear models have been successful in cosmological predictions. Linear models are treated as leading approximation of a complete Taylor series in this paper. If the power series converges quickly, one can freely truncate the series order by order. Detailed convergent analysis on the choices of the expansion parameters is presented in this paper. The related power series for the energy density function, the Hubble parameter and related physical quantities of interest are also computed in this paper.
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