  We give a simple proof of the uniqueness of extensions of good sections for
formal Brieskorn lattices, which can be used in a paper of C. Li, S. Li, and K.
Saito for the proof of convergence in the non-quasihomogeneous polynomial case.
Our proof uses an exponential operator argument as in their paper, although we
do not use polyvector fields nor smooth differential forms. We also present an
apparently simpler algorithm for an inductive calculation of the coefficients
of primitive forms in the Brieskorn-Pham polynomial case. In a previous paper
on the structure of Brieskorn lattices, there were some points which were not
yet very clear, and we give some explanations about these, e.g. on the
existence and the uniqueness of primitive forms associated with good sections,
where we present some rather interesting examples. In Appendix we prove the
uniqueness up to a nonzero constant multiple of the higher residue pairings in
some formal setting which is different from the one in the main theorem. This
is questioned by D. Shklyarov.
