 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-1/3/3-1g/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

a_{- 1}

in the Laurent expansion. At a double pole,

h (z) = (z - z_{0})^{2} f (z)

is holomorphic and

h (z) = h (z_{0}) + h' (z_{0}) (z - z_{0}) + \dots

, so

Res (f, z_{0}) = h' (z_{0})

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