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In 1918 he proved a significant result known as Watson's lemma, that has many applications in the theory on the asymptotic behavior of exponential integrals.
There exists a method for extracting the asymptotic behavior of solutions of Riemann-Hilbert problems, analogous to the method of stationary phase and the method of steepest descent applicable to exponential integrals.
Wörterbuch für Mathematik