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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods

Summer 2024 • Question 5

Question

Math 6720 • Applied Complex Variables and Asymptotic Methods Summer 2024 • Question 5

Compute the complete asymptotic expansion in powers of \(k\) of \[ I(k)=\int _0^\infty e^{-kt^2}\frac {\sin (t^4)}{t^{7/2}}\,dt,\qquad k\to \infty . \]

Raw LaTeX

Compute the complete asymptotic expansion in powers of \(k\) of
\[
I(k)=\int_0^\infty e^{-kt^2}\frac{\sin(t^4)}{t^{7/2}}\,dt,\qquad k\to\infty.
\]

Topic Tags

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