Laurent series Definition and 157 Threads

How does one integrate \int_{}^{} \frac{e^x}{x}dx I could expand it using a Laurent series and than integrating term by term but are there more elementary methods?

Define: \mathbb{C}((t)) = \{t^{-n_0}\sum_{i=0}^{\infty}a_it^i\ :\ n_0 \in \mathbb{N}, a_i \in \mathbb{C}\} What is its algebraic closure? My notes say that it is "close" to: \bigcup _{m \in \mathbb{N}}\mathbb{C}((t))(t^{1/m}) where \mathbb{C}((t))(t^{1/m}) is the extention of the...

Just wondering where to go with this one.. calculate the laurent series of \frac{1}{e^z-1} don't even know where to start on it I know e^z={{\sum^{\infty}}_{j=0}}\frac{z^j}{j!} but not much else...

Hi all,, I have an Exam tommorow and this question is irritating me...Pls help Laurent series of the function f(z)=1/z^2 for |z-a|>|a| .a is not equal to zero... I am waiting for yours responses...I will be highly thankful to you.

I need help with a problem from Complex Analysis. The directions say find the Laurent series that converges for 0<|z|<R and determine the precise region of convergence. The expression is : e^z/(z-z^2). I understand how to do the other 7 problems in this section but not this one. Can someone...

My question is about the coefficients of a complex laurent series. As far as I know, there are three kinds of series: those which converge in a finite circular region around the expansion point z0,(aka taylor series), those that converge in a ring shaped region between two circles centered at...

Does anyone know of any examples of the explicit calculation of the Laurent series of a complex function? Any information would be appreciated.