  For a holomorphic function f on a complex manifold M we explain in this
article that the distribution associated to |f | 2$\alpha$ (Log|f | 2) q f --N
by taking the corresponding limit on the sets {|f | $\ge$ $\epsilon$} when
$\epsilon$ goes to 0, coincides for ($\alpha$) non negative and q, N $\in$ N,
with the value at $\lambda$ = $\alpha$ of the meromorphic extension of the
distribution |f | 2$\lambda$ (Log|f | 2) q f --N. This implies that any
distribution in the D Mmodule generated by such a distribution has the Standard
Extension Property. This implies a non torsion result for the D M-module
generated by such a distribution. As an application of this result we determine
generators for the conjugate modules of the regular holonomic D-modules
associated to z($\sigma$) $\lambda$ , the power $\lambda$, where $\lambda$ is
any complex number, of the (multivalued) root of the universal equation of
degree k, z k + k j=1 (--1) h $\sigma$ h z k--h = 0 whose structure is studied
in [4].
