We know from the foregoing that the denominator of the cone reflectance has at least one root at . We now investigate the ``dc behavior'' more thoroughly.
We already discovered a root at in the denominator in the context of the preceding stability proof. However, note that the numerator also goes to zero at . This indicates a pole-zero cancellation at dc.
and once again the limit is an indeterminate form.
Thus, two poles and zeros cancel at dc, and the dc reflectance is , not as an analysis based only on the scattering filters would indicate.
Both series begin with the term which means both the numerator and denominator have two roots at . Hence, again the conclusion is two pole-zero cancellations at dc.
which approaches as .