So, I was reading the book "Riemann's Zeta Function", by H.M. Edwards, and on page 10 I see an integral I don't quite understand. Here's the integral:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int_{+\infty}^{+\infty} \frac{\left(-x\right)^s}{e^x - 1} \frac{dx}{x}[/tex]

My first problem with this is that, I see an integral from some number to the same number. Shouldn't it be zero?However, the book says that those limits are "intended to create a path of integration which begins at positive infinity, moves to the left down the positive real axis, circles the origin once in the positive (counterclockwise) direction, and returns up the positive real axis to positive infinity." ...what? What does that mean and how can you get that from the integral?

Next, how is that evaluated? The book doesn't give an explanation, simply saying "this integral is equal to that integral, which is equal to this other integral" in essence. I don't understand... I can't even make it past page 10...

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

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!

# Strange (to me) integral

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