I'm trying to plot a recursive sequence namely x(1)=1, x(n+1)=1/2[x(n)+2/x(n)]. I've tried messing around with the \tikzmath library but so far I'm not really successfull. My main issue is properly defining the function, not sure how or even what tool to use to do so. Plotting it is the easy part though.  I'd appreciate any help.
I would like to use pgfplots to create a figure where I plot curves that have a recursive formula. I tried a very simple case that uses the declare function command to see whether this is possible, and I can't compile (TeX capacity exceeded). Is it even possible to do this?  \documentclass{standalone}  \usepackage{pgfplots}  \begin{document}  \begin{tikzpicture}[   declare function={test(\p)=ifthenelse(\p&gt;1, test(\p-1), 0.5);}, ]     \begin{axis}[]     % use TeX as calculator:     \addplot [mark=none] {x};     \addplot [mark=none] {test(0)};     \end{axis} \end{tikzpicture}  \end{document}
How was Will aware of the lights? In  (2016) Will Byers gets taken to the "Upside Down". But he manages to communicate with his mother, e.g through the christmas lights.  &nbsp;   When Joyce is in the cupboard and says "Once for YES, twice for NO.", how would Will make that happen? He can't see his mother, but does he see the lights she is holding?  &nbsp;   Does the alphabet Joyce draws just appear on the wall in the Upside Down, together with the lights?  In the last episode Joyce and Hopper enter the house in the Upside Down, and when they go through the hallway the kids on the other side see the lights go on (suggesting that just standing close to those lights is enough to make them turn on).    But those lights don't seem to be there in the Upside Down.    My Question:   Is there a reasonable explanation on how Will managed to communicate with his mother through the christmas lights? I have a scenario where i want to calculate sum of column   SAL|CAL|TAG|VAL 12.11"|"1.1"|"2.1"|"1.1 13.11"|"1.1"|"2.2"|"2.2 14.11"|"1.1"|"2.4"|"2.4   My below code not giving output giving output as 0.00  I need output for this column CAL VAL  awk -F'|' '{T+=$2} END { printf "%.2f\n", T }' demo.txt   output :  6.7 5.7 How do I install a fingerprint reader on Lenovo ThinkPad? How do I use variables in a sed command? I tried the following code to replace QQ with ZZ, but it doesn't do what I want:  var1=QQ sed -i 's/$var1/ZZ/g' $file   However, this code does what I want:  sed -i 's/QQ/ZZ/g' $file   How do I use variables in sed? Why there's a finite $\Gamma '$ such that $\Gamma ' \vDash \varphi$? Suppose $\Gamma$ is an infinite set of formulas in FOL. It is given that for a structure, $M$: If $\Gamma$ is satisfiable in $M$ then $\varphi$ is valid in $M$.  Why is it true that there's some finite $\Gamma ' \subset \Gamma$, such that $\Gamma ' \vDash \varphi$?   It reminds the compactness theorem in a way, but it's not quite the same. How can I update my OpenGL to 3.0 or higher A simple inequality for floor function Countable union of countable sets(ZF) Area of a quadrilateral proof "Single ampersand used with wrong catcode" error using tikz matrix in beamer Let $G$ be a group and $c$ be a fixed element of $G$. Define a new operation $*$ on G by:   $$x*y=xdy$$   for all $x$ and $y$ in $G$, where $d$ is the inverse of $c$. Prove that $G$ is a group under the operation $*$.    If you want to check, this problem is in the book “A Course In Group Theory”, by John F. Humphreys (problem $3$, page $28$)   I know what are the axioms that $(G,*)$ must obey in order to be a group and I did show that all the axioms where obeyed except the inverse axiom.  My problem is that, whenever I try to verify what would the inverse be for some element $x$, I get an equation where the $x$ is cancelled in both sides.  Can please someone guide me?  Thank you!  (P.S.: This is NOT a homework assignment, I’m studying Group Theory by this book and got problems solving this question) I'm currently passing the pid on the command line to the child, but is there a way to do this in the Win32 API?  Alternatively, can someone alleviate my fear that the pid I'm passing might belong to another process after some time if the parent has died? Date manipulation Function SSJS I want to delete the records from Data Extension based on Date Field in my DE i.e. I want to delete record which were created date before 30 days.But I didn't find date manipulation function in SSJS like dateadd() in ampscript The Half-Elven and their choices Set a polygon's normal's orientation as the objects local rotation orientation (if every polygon is an object) I was told that the following does not work:     Employees having children will be granted a day off.   However, this sounds better:     Having children, those employees will be granted a day off.   What is wrong with the first clause? $x^2$ is congruent to $-1 \bmod p$ In general, how do you solve $x^2$ is congruent to $-1 \bmod p$, where $p$ is an odd prime and $x$ is an integer.  Specifically, I need to solve $x^2\equiv-1 \pmod{29}$ Given that every class gets a minimum of 5 ability score improvements each at levels 4, 8, 12, 16, and 19 (Rogue and Fighter get more at other levels), do these ability score improvements occur by character level or by class level?  For example, is it possible to create a character who never once gains a single ability score improvement by reaching level 3 in a class and then switching to a different class repeatedly?  I had originally thought the 5 that every class gets would occur by character level, so for example a sorcerer1/bard3 would earn an ability score improvement for reaching character level 4. But there are others who have expressed the opinion that this is wrong. Is it possible to add non-number characters on the left of a code block?  Specifically, I want to add ... to correspond with some source code (see image).    I am currently using commands to stop / start the line numbers. Here is the code:  \documentclass[12pt]{article}  \usepackage[a4paper, margin = 20mm, top = 30mm, bottom = 25mm]{geometry} \usepackage{xcolor, soul} \usepackage{listings}  \definecolor{codebackground}{rgb}{0.95, 0.95, 0.92}  \lstset {     frame            = tb, % hrule above and below     keepspaces       = true,     columns          = flexible,     basicstyle       = {\normalsize\ttfamily},     escapeinside     = {(*@}{@*)}, % for escaping     backgroundcolor  = \color{codebackground},     showstringspaces = false,     language         = C,     keywordstyle     = \color{blue},     stringstyle      = \color{red},     commentstyle     = \color{teal},     numbers          = left, % {none, left, right}     firstnumber      = 1,     numberstyle      = \scriptsize\color{black},     numbersep        = 5pt }  \let\origthelstnumber\thelstnumber \makeatletter % for stopping line numbers \newcommand*\stopnumber {     \lst@AddToHook{OnNewLine}     {         \let\thelstnumber\relax         \advance\c@lstnumber-\@ne\relax     } } % for starting line numbers \newcommand*\startnumber[1] {     \setcounter{lstnumber}{\numexpr#1-1\relax}     \lst@AddToHook{OnNewLine}     {         \let\thelstnumber\origthelstnumber         \refstepcounter{lstnumber}     } } \makeatother  \begin{document} \begin{lstlisting}[firstnumber = 456] int third_function(const int c) {     /* error checking */     if(c &lt; 0)     {         return;     } (*@ \stopnumber @*)      ...     (*@ \startnumber{512} @*)     /* other stuff */     int d = 4;     char* word = "third function"; (*@ \stopnumber @*)      ...     (*@ \startnumber{678} @*)     return (c * d); } \end{lstlisting} \end{document} Can the union axiom be weakened?