 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-2/7e/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

By the transformed equation, infinity is ordinary precisely when

\frac{2}{t} - \frac{p ( 1/ t )}{t ^{2}}, \frac{q ( 1/ t )}{t ^{4}}

are holomorphic at

t = 0

. Equivalently, as convergent Laurent expansions near infinity,

p (z) = \frac{2}{z} + O (z^{- 2}), q (z) = O (z^{- 4}) .

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