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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/30d/d/solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 30D / d / Solution by

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

The saddle contributes the full Gaussian

e^{i x} \int_{- \infty}^{\infty} e^{- x s^{2} /2} d s = 2 π, x^{- 1/2} e^{i x} .

(1)

Thus $α = 2 π$ . Since the phase is exactly quadratic, there are no further algebraic saddle terms; the next contribution is the endpoint term $O (x^{- 1} e^{- 3 x /2})$ .

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