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...