A system of linear differential equations
 |
(1)
|
with 
an analytic 
matrix, for which the matrix 
is analytic in 
and has a pole
of order 1 at 
for 
,
..., 
.
A system is Fuchsian iff there exist 
matrices 
, ..., 
with entries in 
such that
 |
(2)
|
 |
(3)
|
