Take the 2-minute tour ×
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 was asked a question that I am pretty sure has a catch. I was asked how would the series representations of certain complex functions be affected by the choice of branch. My understanding is that the series representation, where it exists, is unique, so it really doesn't matter which branch one chooses, but I don't think that is what they are looking for. Consider the familiar function $\ln (1+z)$ for example? Thank you.

share|improve this question
1  
for $\ln(1+z)\ $ the branch will add an offset of $2 k \pi i\ $ for the k-th branch. In other cases it may be more complicated : the Lambert W branches $W_0$ and $W_{-1}$ are rather different –  Raymond Manzoni Feb 19 '12 at 12:08
    
@RaymondManzoni: So the uniqueness theorem is only applicable to within a branch? –  tycho Feb 19 '12 at 12:14
    
Well Taylor and Laurent series are unique in the disk or annulus where they are valid. Perhaps that this Wikipedia entry on branch points will help you. –  Raymond Manzoni Feb 19 '12 at 12:40
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.