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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Spring 2013 • Question 10

Question

Math 6420 • PDE Spring 2013 • Question 10

Find at least three terms of the asymptotic expansion of the integral \[ I(s)=\int _0^1 \ln t\, e^{ist}\,dt, \qquad s\text { is real and }s\to +\infty . \]

Raw LaTeX

Find at least three terms of the asymptotic expansion of the integral
\[
  I(s)=\int_0^1 \ln t\, e^{ist}\,dt,
  \qquad s\text{ is real and }s\to+\infty.
\]

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