Portions of this entry contributed by Vinod Krishan
A second-order ordinary differential equation Eric Weisstein's World of Math that applies to polytropic profiles in density, defined as those which have the form
where P is pressure, K is a constant, is the density, and
with n is an integer (Chandrasekhar 1960).
References
Chandrasekhar, S. Radiative Transfer. New York: Dover, 1960.
Krishan, V. (Ed.) Astrophysical Plasmas and Fluids. Dordrecht, Netherlands: Kluwer, 1999.