When one uses a contour integral to evaluate an integral on the real line, for example [tex]\int_{-\infty}^{\infty}\frac{dz}{(1+x)^{3}}[/tex] is it correct to say that one analytically continues the integrand onto the complex plane and integrate it over a closed contour ##C## (over a semi-circle of radius ##R## closed along the real line between ##-R## and ##R##)? In this case [tex]\int_{C}\frac{dz}{(1+z)^{3}}[/tex] which reduces to the original integral on the real line in the limit as the radius tends to infinity.(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Contour integration & the residue theorem

**Physics Forums | Science Articles, Homework Help, Discussion**