Solution
= Solution
One form of <Watson lemma> is this. If $f(t)$ has the asymptotic expansion $f(t)\sim\sum_{n\geq0}a_nt^{λ_n-1}$ as $t\downarrow0$, with $0<λ_0<λ_1<\cdots$, and the Laplace integral has suitable growth control away from zero, then
$$
\int_0^b e^{-xt}f(t)\,dt\sim\sum_{n\geq0}a_nΓ(λ_n)x^{-λ_n}
$$
as $x\to∞$, with truncation after any fixed number of terms justified by the corresponding remainder estimate.