8.5 Existence of expansions using Fuchsian methods, S2 × S1 and S3 cases
There are results concerning the existence of expansions in the S2 × S1 and S3 cases as well .
However, the analysis is complicated by the presence of the axes; regularity conditions lead to the
requirement that the velocity has to be either –1 or 3 there. As a consequence, the result is different, since
such values of the velocity are inconsistent with expansions containing the full number of free functions. We
refer the reader interested in more details to .