Sign up ×
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.

I need to show that $$\lim_{R \to \infty}\int_{\gamma}\frac{1}{q(z)}dz=0$$ using the estimation lemma.

How would I show the above? I think to approach this i need to change $q(z)$ into only terms of $z$ and substitute it into the estimation lemma, but how would I do that? Thanks.

share|cite|improve this question

1 Answer 1

up vote 1 down vote accepted

We have $$ \left| \int_\gamma 1/q(z) \right|< \frac{2 \pi R}{ \min \limits_{|z|=R}|q(z)| }.$$ Now, $|q(z)|\ge R^2-|a|R-|b|>R^2/2 $ for very large values of $R$. Thus, $\left|\int_\gamma 1/q(z) \right|< 4\pi/R\to 0$.

share|cite|improve this answer

Your Answer


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.