The high temperature series for the free energy of a type II superconductor based on the Landau-Ginzburg free energy functional, is analyzed in an attempt to find the behaviour near H_c2. Rules for calculation of the terms of the series are given and the first six terms of the series are evaluated. The series are obtained both for bulk and thin film superconductors and are compared with the corresponding series for one-dimensional and zero-dimensional Landau-Ginzburg systems. Analysis of the series by Pade approximants suggests that there is no singularity of the free energy for real temperatures and so no sharp critical field. An attempt is made by use of Pade and Borel-Pade approximants to extrapolate the series below the transition temperature to the region of the flux lattice and the results are fairly consistent but not altogether convincing.