Is there an anti derivative function to the complex function   $$f(z)=\frac{z}{(z-1)(z-2)}$$ in $|z|&gt;4$?   My attempt: We notice that $f(z)=\frac{z}{z-2}+\frac{z}{1-z}$ (by decomposing to partial fractions). But when I try to guess an anti-derivative function it doesn't go well: $$ (\ln(\frac{1}{1-z})'=\frac{1}{1-x} \\(\ln\frac{z}{1-z})'=\frac{1}{x(1-x)} $$
Let $f(z)=\frac{1}{(z-1)(z-2)}$ and $g(z)=\frac{z}{(z-1)(z-2)}$. Let $\gamma$ be the circle of radius 4 centered at the origin and traveled once in the counterclockwise direction. Let $A=\{ z \in \mathbb{C}: |z|&gt;3 \}$  1) I need to show there is no analytic function $G: A \to \mathbb{C}$ such that $G'(z)=g(z)$ for all $z$ in $A$.   2) I also need to show that there is an analytic function $F:A \to \mathbb{C}$ such that $F'(z)=f(z)$ for all $z$ in $A$.  Do I have to integrate to find such function?
Performing reverse clip in ArcMap? Is there a way to perform a 'reverse' of the clip function in ArcMap?  I am not exactly sure how to explain this so here is a diagram: New figure environment I am writing my PhD thesis. In my manuscript I have Figures in the text and Photographic plates (a figure of figures) in the annexes. The two elements are different and I would like create a new environment of Plate that follows the same structure of the Figure environment. Where can I find the Figure environment to modify it?  The new environment table should have exactly the same structure than the figure environment but replacing the word figure by the word Planche (in French). How do I create a dynamic key to be added to a JavaScript object variable Turn off paragraph indention for a single line Is it possible to turn off the paragraph indention for a single line? I have the following use case: I open a new section which describes the task of an exercise. Since I use the font size \large for the section I don't want to use the section text for the task description.  Therefore I added the task description after the section. The disadvantage is that an indention is created when starting to write text after the task description.  What are possible solutions to this problem? Why doesn't the Related question list show that questions are closed? How can I explain to a non-native why the plural of a noun isn't used adjectivally? How can I explain to a non-native speaker that while this is correct:     The felling of trees.    And this is also correct:     tree felling   This is not:     *trees felling   To a non-native it seems very reasonable that since many trees are being felled and given that the felling of trees uses the plural, the inverse form would also use the plural and become trees felling.  To a native speaker such as myself, the latter is very obviously wrong, but I couldn't figure out how to formalize this into a rule that a non-native can understand. How do I uninstall Ubuntu Wubi? "The package lists or status file could not be parsed or opened" Everytime I sudo apt-get update it always not complete and will say in the end  E: Read error - read (5: Input/output error) E: The package lists or status file could not be parsed or opened.   Same goes, when I try to install something and do sudo apt-get install &lt;some app&gt;  What should I do ? I admit, that my drive has bad sectors, could that be the reason? Is there anything else I can do? Can any linear transformation be represented by a matrix? Use $\cal L$ to denote a linear transformation on some vector space. We know any matrix $\bf{A}$ can be viewed as a linear transformation by defining $\cal L:= \cal L(\bf{v})= Av$ where $\bf{v}$ is a vector. I am curious is any linear transformation can be represented by a matrix? If so, why? If not, can anyone help provide a counterexample?  In particular, projection of vectors onto a vector $\bf{b}$ is a linear transformation defined by ${\cal L(\bf{v})}=({\mathbf{v}} \cdot \frac{{\mathbf{b}}}{{|{\mathbf{b}}|}})\frac{{\mathbf{b}}}{{|{\mathbf{b}}|}}$. Can this linear transformation be represented by a matrix?  Thank you! Can I use lens brand X on interchangeable lens camera brand Y? After installing NVIDIA driver, X isn't showing I recently installed the NVIDIA 319 driver from the Jockey window, and now X won't load! I'm stuck with a blinking cursor. I used to have the 304 drivers installed.  How do I fix this? From time to time I lose all edits because of undo in Object Mode. If I enter immediately after Undo in Edit Mode I can't redo, and switching again in Object results in losing all edit history.  How can I resolve this? Separating undo history by mode or linear/unified will both be acceptable.  Edit:I think the most preferable solution will be to disable/skip edit undos when in object mode through an addon. What do brokers do with bad stock? How do I edit a file in /proc that can be viewed with cat, but is not editable by mousepad and abiword? I can show this best by a picture:    This cross also shows when I export it as raster or pdf. What is it and how can I get rid of it?  I am using Qgis 2.4 and the map was done with the help of the Grass plugin AniMove on Linux Mint. How to install wps office via terminal? It's pretty complicated and sometimes the system freezes when I try to download and install wps office. I think it is much more convenient to use the terminal. But I never used installed WPS Office from the command line. That would be great if I could update it using software manager or terminal. Third party deb files are from separate locations. I specifically want to know about WPS Ugly 'post date' alignment on user profile when the date wraps into multiple lines From      Every linear function on a finite-dimensional space is continuous.   I was wondering what the domain and codomain of such linear function are?   Are they any two topological vector spaces (not necessarily the same), as along as the domain is finite-dimensional? Can the codomain be a different normed space (and may not be finite-dimensional)?  I asked this because I saw elsewhere the same statement except the domain is a finite-dimensional normed space, and am also not sure if the codomain can be a different normed space (and may not be finite-dimensional).  Thanks and regards! Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$ If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative Let $R$ be a ring such that for every $x\in R$ we have $x^2-x \in Z(G)$. Show that $R$ is a commutative ring.    My thoughts  What should I do? I could show that every $y \in R$ could be written in the shape $x^2-x$ but I don't know if that is true. We know that  $y \cdot(x^2-x) \ = \ (x^2-x)\cdot y$ for any $x,y \in R$, but that doesn't mean that $xy = yx$. Please give me a hint