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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2007 • Question 10

Question

Math 6420 • PDE Fall 2007 • Question 10

Find the two-term asymptotic expansion of the integral \[ I(s)=\int _{-\infty }^{\infty }\frac {e^{s(ix+1)^2}}{(x+i)^2}\,dx, \qquad s\text { is real and }s\to +\infty . \]

Raw LaTeX

Find the two-term asymptotic expansion of the integral
\[
  I(s)=\int_{-\infty}^{\infty}\frac{e^{s(ix+1)^2}}{(x+i)^2}\,dx,
  \qquad s\text{ is real and }s\to+\infty.
\]

Topic Tags

Cauchy Integral Formula and Integral Theorems Linear Programming and Optimization Real Integral Evaluation by Complex Methods Watson's Lemma and Laplace's Method