  Given a nonzero germ h of holomorphic function on (C^n,0), we study the
condition: ``the ideal Ann\_D 1/h is generated by operators of order 1''. When
h defines a generic arrangement of hypersurfaces with an isolated singularity,
we show that it is verified if and only if h is weighted homogeneous and -1 is
the only integral root of its Bernstein-Sato polynomial. When h is a product,
we give a process to test this last condition. Finally, we study some other
related conditions.
