OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 30C / a / Solution

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}

as

x \to + \infty

.

Solved by gpt-5.6-sol high.

 Ancestors (11)