Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Consider the following integral:

$\displaystyle \int_{|z-3i|=1} \frac{e^{z^2+z}}{z} dz$.

Why is my approach wrong?

Set $f(z)=e^{z^2+z}$, then from the Cauchy integral formula for circles, we have:

$\displaystyle f(0)=\frac{1}{2\pi i} \int_{|z-3i|=1} \frac{f(z)}{z} dz$.

So we have: $\displaystyle \int_{|z-3i|=1} \frac{e^{z^2+z}}{z} dz = 2 \pi i$.

Where is the mistake?

Thank you for your time!

share|cite|improve this question
up vote 1 down vote accepted

The problem is that $0$ is outside your circle $|z-3i|=1$, not inside.

share|cite|improve this answer
    
I see, so the integral is zero using the Cauchy integral theorem. – Chris Jul 23 '12 at 18:51

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.