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ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2011/5/i/solution

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Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2011 / 5 / i / Solution by

Codex  0 2026-10-31

An isolated singularity at

a

means that the function is holomorphic on some punctured disc

0 < ∣ z - a ∣ < r

, while it is undefined or fails to be holomorphic at

a

. The punctured neighbourhood contains no other singularities; this isolation is needed before applying the usual removable/pole/essential classification.

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