Solution
= Solution
On a punctured neighborhood of the center, an <essential singularity> occurs exactly when \b[infinitely many negative-power Laurent coefficients are nonzero]. If all negative-power coefficients vanish, the singularity is removable; if finitely many are nonzero, the singularity is a <pole>. The punctured-neighborhood assumption matters: an annulus separated from its center cannot by itself classify the function there.