Cosmological Applications of Pade Approximant
  As is well known, in mathematics, any function could be approximated by the
Pad\'e approximant. The Pad\'e approximant is the best approximation of a
function by a rational function of given order. In fact, the Pad\'e approximant
often gives better approximation of the function than truncating its Taylor
series, and it may still work where the Taylor series does not converge. In the
present work, we consider the Pad\'e approximant in two issues. First, we
obtain the analytical approximation of the luminosity distance for the flat
XCDM model, and find that the relative error is fairly small. Second, we
propose several parameterizations for the equation-of-state parameter (EoS) of
dark energy based on the Pad\'e approximant. They are well motivated from the
mathematical and physical points of view. We confront these EoS
parameterizations with the latest observational data, and find that they can
work well. In these practices, we show that the Pad\'e approximant could be an
useful tool in cosmology, and it deserves further investigation.
