Tell me more ×
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.
up vote 3 down vote favorite

Well, I have no idea: Does $\tan(1/z)$ have a Laurent series convergent on $0<|z|<R$?

share|improve this question
It is preferable to use \tan, \sin, \log, \cos, \exp etc in math mode instead of tan, sin, log, cos, exp etc – user17762 Jun 10 '12 at 5:35
ok, thank you, i did not know that. – Taxi Driver Jun 10 '12 at 5:39
1  
Where does it have poles? – WimC Jun 10 '12 at 6:08

1 Answer

up vote 5 down vote accepted

In short, the answer is no. The function $\tan(1/z)$ has poles at $z=\frac{1}{\pi/2+n\pi}$, which means that it is not analytic on the annulas you mentioned for any $R$.

share|improve this answer

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.