A Polytropic Approach to Semi-relativistic Isothermal Gas Spheres at
  Arbitrary Temperature
  We use standard polynomial expansion technique to show the existence of a
relation between polytropic model and the description of gas spheres at finite
temperature. A numerical analysis is made concerning the obtained perturbative
parameters. It is shown that there is a correspondence between polytropic and
gas sphere thermal models for fermions and bosons. For instance, the polytropic
index $n$ displays evident correlation with temperature and chemical potential.
