Watson's lemma

In mathematics, Watson's lemma, proved by G. N. Watson (1918, p. 133), has significant application within the theory on the asymptotic behavior of integrals.

Let ${\displaystyle 0<T\leq \infty }$ be fixed. Assume ${\displaystyle \phi (t)=t^{\lambda }\,g(t)}$, where ${\displaystyle g(t)}$ has an infinite number of derivatives in the neighborhood of ${\displaystyle t=0}$, with ${\displaystyle g(0)\neq 0}$, and ${\displaystyle \lambda >-1}$.

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