 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/30c/a/solution

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

Watson lemma states that if, near zero,

f (t) \sim \sum_{n = 0}^{\infty} a_{n} t^{n + λ - 1}, λ > 0,

and the tail is suitably controlled, then

\int_{0}^{b} e^{- x t} f (t) d t \sim \sum_{n = 0}^{\infty} a_{n} Γ (n + λ) x^{- n - λ}

x \to + \infty

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