Javascript Regex object and the dollar symbol
Why do regex constructors need to be double escaped?
Suppose that   $$f(x)=1+\sum_{n=1}^\infty a_n \frac{x^n}{n!}\ \ \forall \ x\in \mathbb{R}$$   where $\sup_{x&gt;0}\left|e^xf(x)\right| &lt; \infty$ and $\sup_{n\in\mathbb{N}} |a_n|&lt; \infty$.      Prove that $a_n = (-1)^n$ , $\forall n\in \mathbb{N}$   It seems amazing to me. What we need to prove is $f(x)=e^{-x}$. It seems insufficient to prove this strong conclusion, but actually it is true and all the "counterexamples" I found were wrong.  My attempt  Put $g(x)=e^x f(x)$. $$\left|g^{(n)}(0)\right|=\left|\sum_{k=0}^n \binom{n}{k} f^{(k)}(0)\right|\le 2^n\sup_{n\in\mathbb{N}} |a_n|  $$ Put $h(x)=g(\frac{x}{2})$. Thus  $$h^{(n)}(0)=\frac{1}{2^n}g(0) \le \sup_{n\in\mathbb{N}} |a_n|$$ which implies that $$h(x)=1+\sum_{n=1}^\infty b_n \frac{x^n}{n!}\ \ \forall \ x\in \mathbb{R}$$ where $$|b_n|\le \sup_{n\in\mathbb{N}} |a_n| \ \ \forall \ n\in\mathbb{N}  \,\,\,\,\,\&amp; \,\,\,\,\,  \sup_{x&gt;0}\left|h(x)\right| &lt; \infty $$   And hence if $b_k&lt;0$, then there exists $l&gt;k$ such that $b_l&gt;0$. I want to yield a contradiction by supposing this, but I failed.  Any hints or other new ideas? Thanks in advance!   (I heard that this problem can be solved by complex analysis. This is the reason why I attach the complex-analysis tag.) How to Join Games with Minecraft Pocket Edition 0.7 Showing the sequence converges to the square root For any $a &gt; 0$, I have to show the sequence $x_{n+1}$ $=$  $ \frac 12$($x_n+ $ $ \frac {a} {x_n}$)  converges to the square root of $a$ for any $x_1&gt;0$.  If I assume the limit exists ( denoted by $x$) then,  $x$ $=$  $ \frac 12$($x+ $ $ \frac {a} {x}$) can be solved to $x^2 = a$  How could I show that it does exist? how can i display the latest items from another site collection I have a web application, with three site collections . and i want inside my team site to be able to display the latest pages that  have been added to my enterprise wiki site collection. so what are the available approaches which i can follow?  Thanks in advance for any help.  Regards How to get git-completion.bash to work on Mac OS X? I have followed  to  add git-completion.bash to my /opt/local/etc/bash_completion.d/git-completion  and I put PS1='\h:\W$(__git_ps1 "(%s)") \u\$ ' in my .bashrc_profile  But now I am getting this -bash: __git_ps1: command not found everything I do a cd.  Can you please tell me what am I missing? What is polarisation, spin, helicity, chirality and parity? Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what these quantities mean and how they are related? What are the values for e.g. basic particles like electron or photon? Man/Tree Symbiosis It was an old book... I'm pretty sure it was a book, and pre-1990's I think. The basic plot was this man somehow interacted with this tree, and as a result he became a carrier of the tree's 'seed'. They were in a symbiotic relationship: the man got a much longer life, more strength, etc.; but when he did die the tree would grow up from his body. I am new to linux, but had a question. I am getting in the business of buying old computers, putting Linux on them, then donating them to students who don't have their own computer at home. I have gone through and installed Xubuntu on my system, installed/uninstalled all the software that I want/need, and now want to know if there is a way that I could make an ISO of my system, and put it onto ANOTHER computer, and still have all of my tweaks, and programs ready to go after the ISO has installed. That way I don't need to go through and spend an hour or two on every computer.   What programs would you recommend for creating an ISO like this?   Thanks, Tobin How to import a module given its name as string? I'm writing a Python application that takes as a command as an argument, for example:  $ python myapp.py command1   I want the application to be extensible, that is, to be able to add new modules that implement new commands without having to change the main application source. The tree looks something like:  myapp/     __init__.py     commands/         __init__.py         command1.py         command2.py     foo.py     bar.py   So I want the application to find the available command modules at runtime and execute the appropriate one.  Python defines an __import__ function, which takes a string for a module name:     __import__(name, globals=None, locals=None, fromlist=(), level=0)      The function imports the module name, potentially using the given globals and locals to determine how to interpret the name in a package context. The fromlist gives the names of objects or submodules that should be imported from the module given by name.       Source:    So currently I have something like:  command = sys.argv[1] try:     command_module = __import__("myapp.commands.%s" % command, fromlist=["myapp.commands"]) except ImportError:     # Display error message  command_module.run()   This works just fine, I'm just wondering if there is possibly a more idiomatic way to accomplish what we are doing with this code.  Note that I specifically don't want to get in to using eggs or extension points. This is not an open-source project and I don't expect there to be "plugins". The point is to simplify the main application code and remove the need to modify it each time a new command module is added. If $G$ has no proper subgroup, prove that $G$ is cyclic of order $p$, where $p$ is a prime number.     I know that since $G $is a group with no proper subgroups, $g \in G$ is not just the identity. I don't know where to go from there. Show Capslock on Windows 8 Books on cosmology I have finished Carroll's general relativity book, Spacetime and Geometry. I am specifically interested in cosmology, so is there any book which goes more in depth into cosmology? I prefer a mathematically rigorous book, which goes beyond the cosmology chapter in Carroll's book. The Big Bang and inflation theory should be dealt with in depth. In Python, how do I get a function name as a string, without calling the function?  def my_function():     pass  print get_function_name_as_string(my_function) # my_function is not in quotes   should output "my_function".  Is such function available in Python? If not, any ideas on how to implement get_function_name_as_string, in Python? 'both in terms of' or 'in terms of both'? Setting a document in MS Word-12pt (12bp) Warning  If you're looking for advice how to make your document look like it's been written in Word, this is most likely not the question you're looking for. This question is mostly of theoretical nature, as it results in tiny differences, which will most likely not be noticed by someone who doesn't allow the use of LaTeX.  Questions that might be more helpful for this matter are:           Question  I learned that MS Word uses a slightly different version of the unit "point" (pt) than TeX does:     The 12 point of Word will be PostScript point, which in TeX would be called 12bp. A TeX pt is slightly smaller: it's 1/72.27 inch, while a bp/PostScript point is 1/72 inch. See also    ( in )  I'm writing a paper that would usually be expected to be "typeset" in MS Word, thus I want to use the same font size as Word would.  How do I set a document e.g. in the "12pt" font size that MS Word would use?  In case it matters, I'm using the article document class, Latin Modern (lmodern) as a font with the T1 font encoding and compile with pdfLaTeX, but input on different set-ups is more than welcome. Will higher temperatures damage a computer over time, even when not reaching the maximum temperature? For example, if the maximum is 105 degrees celcius, will the computer break faster when continually having it on 80 degrees celsius instead of, for example, 60 degrees celcius. How to show $\lim_{n \to \infty} a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} = x/2$? This question came from the prelim exam I took last month. I have a proof that seems a bit unwieldy to me (posted as an answer), so I'm opening it up to ask if there are other ways of showing this.     Let $x$ be any positive real number, and define a sequence $\{a_n\}$ by   $$ a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} $$   where $[x]$ is the largest integer less than or equal to $x$. Prove that $\displaystyle{\lim_{n \to \infty} a_n = x/2}$. Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$ I know that the improper integral  $$ \int_0^\infty\frac{1}{(1+x^2)^s}\,dx $$ is convergent for $s&gt;0.5$ and divergent otherwise. Furthermore, it has a closed form for $s \in \mathbb{N}$ (this can be obtained using the Residue Theorem). My question is to know whether it has a closed form for any non-integer $s &gt;0.5$. If I was at point $A$ and I wanted to walk directly to point $B$, I would have to walk half way to point $B$, but before that I would have to walk half way to halfway to halfway to point $B$ and half of that again and so on and so fourth. if I halved this distance an infinite amount of times then there would be an infinite amount of actions I would need to perform in order to cross from $A$ to $B$. Therefore, if each action took any quantity of time at all, then it would take me an infinite amount of time to cross from $A$ to $B$, even if $A$ and $B$ were only a few centimetres apart!   Because I am not infinitely old and I can move, there must be a flaw in this logic. Where is it? I posted this question but for some reason I can't get back into my account:    Most things I see with 220V have both hot legs going through the switch or relay, current "returns" through the switch.  Is it against code to wire one leg directly to the equipment and the other leg is switched as opposed to having both legs switched.  It seems useless and a waste of wire to switch both legs.  Basically  vs  (minus the GFCI as I'm not allowed to have that)  As a bonus question.  I assume I need a "motor rated switch" as standard switches can weld due to the high startup current.  Is  one legal\safe?