Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

I need to show that:

[tex] \int_{0}^{\infty } \frac{x^{a}}{(x+1)^2} \dx = \frac{\pi a}{\sin(\pi a)} [/tex]

, where -1<a<1.

The problem is, that although a hint is given,the path of integrating it, I have difficulty what they really mean with "cut line, branch points, multivalued functions" etc.

In the hint , the path of integration is the following, which I don't understand why they have chosen it like this, could some explain their reasoning? For example, why do they exclude z=-1?

http://img143.imageshack.us/img143/151/acf1.jpg [Broken]

EDIT:

I have now calculated this integral using my own , simpler, contour, which is basically the same as this one, except it includes the point z=-1 ( Which I still don't understand why my book excludes..).

By the way; the whole idea of branch cuts etc basically means that if you wounded one time around the origin, you have to use z=r*exp(i(theta+2pi)); is this right? I calculated using this and I got the correct answer..

**Physics Forums - The Fusion of Science and Community**

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!

# Complex integration, branch cuts

Loading...

Similar Threads - Complex integration branch | Date |
---|---|

I Complex integral | Jun 8, 2017 |

I Complex integral of a real integrand | May 5, 2017 |

A Inverse Laplace transform of a piecewise defined function | Feb 17, 2017 |

I Question about Complex limits of definite integrals | Jan 30, 2017 |

A A problem about branch cut in contour integral | Dec 5, 2016 |

**Physics Forums - The Fusion of Science and Community**