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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2004 • Question 7

Question

Math 6420 • PDE Fall 2004 • Question 7

Obtain the inverse Laplace transform of the function \[ \widehat {F}(s)=s^{-a},\qquad 0<a<1 \] by evaluating the associated Bromwich contour integral with a branch cut along the negative real axis. Express the answer in terms of the gamma function \[ \Gamma (z)=\int _0^\infty t^{z-1}e^{-t}\,dt. \]

Raw LaTeX

Obtain the inverse Laplace transform of the function
\[
  \widehat{F}(s)=s^{-a},\qquad 0<a<1
\]
by evaluating the associated Bromwich contour integral with a branch cut along the negative
real axis. Express the answer in terms of the gamma function
\[
  \Gamma(z)=\int_0^\infty t^{z-1}e^{-t}\,dt.
\]

Topic Tags

Cauchy Integral Formula and Integral Theorems Laplace Equation Linear Programming and Optimization Real Integral Evaluation by Complex Methods