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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 7D / b / Solution

Using the convention adopted here, the Hilbert transform is

H f (y) = \frac{1}{π} PV \int_{- \infty}^{\infty} \frac{f ( x )}{y - x} d x .

The convention with denominator

x - y

differs by a minus sign.

Solved by gpt-5.6-sol high.

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