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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods

Summer 2021 • Question 5

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods Summer 2021 • Question 5
Asymptotic expansions Find the complete asymptotic expansion of \[ I(k)=\int_0^\infty e^{-kt}t^{-1/3}\cos t\,dt,\qquad k\to\infty. \]

Raw LaTeX

Asymptotic expansions

Find the complete asymptotic expansion of
\[I(k)=\int_0^\infty e^{-kt}t^{-1/3}\cos t\,dt,\qquad k\to\infty.\]
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Topic Tags

Real Integral Evaluation by Complex Methods Watson's Lemma and Laplace's Method