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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 7E / b / i / Solution

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}) .

Solved by gpt-5.6-sol high.

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