This concept classifies isolated singularities of analytic functions—points where a function fails to be analytic but is analytic on some punctured disk around them—into removable singularities, poles of order n, and essential singularities, based on the structure of negative-power coefficients in the function's Laurent expansion. It also establishes characterization theorems: boundedness near a singularity implies it is removable (Riemann's theorem), equivalent conditions for a pole of order n, and that a singularity is a pole if and only if the function's modulus tends to infinity there. It belongs to complex analysis, building directly on Laurent series theory and forming the foundation for later residue theory.
This concept classifies isolated singularities of analytic functions—points where a function fails to be analytic but is analytic on some punctured disk around them—into removable singularities, pole…