A function holomorphic on an annulus r < |z − a| < R expands as Σ_{n=-∞}^∞ c_n (z − a)^n. Encodes singularities: the negative-power coefficients (principal part) classify poles vs essential singularities.
A function holomorphic on an annulus r < |z − a| < R expands as Σ_{n=-∞}^∞ c_n (z − a)^n. Encodes singularities: the negative-power coefficients (principal part) classify poles vs essential singularities.