Formal Symbol Type Solutions of Fuchsian Microdifferential Equations

We construct a basis of solutions for a micro-differ- ential equation with Fuchsian singularities in microfunctions with one holomorphic parameter. More precisely, we construct solutions writ- ten by formal symbols with one holomorphic parameter. For such an equation of order m, we get (m−1)-regular formal symbols and one sin- gular formal symbol; the latter is not holomorphic along the Fuchsian singularities but has boundary values in the sense of microfunctions.