  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.
