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Latex Example Use in a Jupyter Notebook
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "<font color=\"red\"><H1>LATEX INFO</H1></font>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "In new Jupyter notebooks I have been working you can just type latex in markdown cells and it works." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| " No need for `%%latex` in a code cell then. --> see very first line of TD's answer at http://stackoverflow.com/questions/13208286/how-to-write-latex-in-ipython-notebook" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Example of new way on next line, but won't work in old canopy I have on home computer. \n", | |
| "(kept old one so far because lets me edit directly in cnaopy whereas new Canopy goes to browser and is a bit annoying in opening and closing.) \n", | |
| "To see it work, easiest way is to upload to tmpnb.org and use there." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "\\begin{aligned}\n", | |
| "\\nabla \\times \\vec{\\mathbf{B}} -\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{E}}}{\\partial t} & = \\frac{4\\pi}{c}\\vec{\\mathbf{j}} \\\\\n", | |
| "\\nabla \\cdot \\vec{\\mathbf{E}} & = 4 \\pi \\rho \\\\\n", | |
| "\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n", | |
| "\\nabla \\cdot \\vec{\\mathbf{B}} & = 0\n", | |
| "\\end{aligned}" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Just verified it works there. The only issue is why it puts a line next to the right side latex cell? ---> Known issue in Chrome that should eventullay resolved without need to do anything, see http://stackoverflow.com/questions/35171714/ipython-jupyter-notebook-producing-ghost-line-in-all-equations" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Also see it used in the notebook `Fishers exact test in Jupyter notebook.ipynb` which currently only works at work computer or by uploading to tmpnb.org, but I hope to eventually laso have it on `binder.org`" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**Easy Equation writing examples**\n", | |
| "\n", | |
| "\n", | |
| "$$c = \\sqrt{a^2 + b^2}$$\n", | |
| "\n", | |
| "Logarithmic growth of a population of cells can be described mathematically as\n", | |
| "$$N = N_oe^{ln2(t/t_2)}$$\n", | |
| "(from page 177 of Methods in Yeast Genetics, 205 Edition) \n", | |
| "\n", | |
| "**See [here](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference) for an awesome reference for MathJax **" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "\"and use single $\\$\\ (rather than double $\\$\\$\\) to keep the equation in-line. stackoverflow.com/q/19412644/1224255\" - from http://stackoverflow.com/questions/13208286/how-to-write-latex-in-ipython-notebook (<---this itself was tricky to write and I had to use minrk's April 18th answer at https://github.com/ipython/ipython/issues/3197/ as a basis" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "source": [ | |
| "Based on [here](https://tex.stackexchange.com/questions/158897/how-do-i-get-a-hyphen-in-mathrm) I figured out (probably again) how to add hyphen when in math mode in Jupyter notebooks and not have it loolike a minus sign.\n", | |
| "\n", | |
| "$$\\frac{mito\\ purification\\ RNA\\textrm-Seq\\ data}{total\\ cell\\ RNA\\textrm-seq\\ data}$$\n", | |
| "\n", | |
| "VS. \n", | |
| "\n", | |
| "$$\\frac{obs_a - obs_b}{exp_a - exp_b}$$\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/latex": [ | |
| "The mass-energy equivalence is described by the famous equation\n", | |
| " \n", | |
| "$$E=mc^2$$\n", | |
| " \n", | |
| "discovered in 1905 by Albert Einstein. \n", | |
| "In natural units ($c$ = 1), the formula expresses the identity\n", | |
| " \n", | |
| "\\begin{equation}\n", | |
| "E=m\n", | |
| "\\end{equation}" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.Latex object>" | |
| ] | |
| }, | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "#from JupyterLab demo notebook November 2, 2016\n", | |
| "from IPython.display import Latex\n", | |
| "Latex('''The mass-energy equivalence is described by the famous equation\n", | |
| " \n", | |
| "$$E=mc^2$$\n", | |
| " \n", | |
| "discovered in 1905 by Albert Einstein. \n", | |
| "In natural units ($c$ = 1), the formula expresses the identity\n", | |
| " \n", | |
| "\\\\begin{equation}\n", | |
| "E=m\n", | |
| "\\\\end{equation}''')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "**Below is old stuff I had in this notebook before Jupyter and new way of putting latex in a markdown cell as described above**" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "(Link on cell on next line seems to lead to dead link now???)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "from http://nbviewer.ipython.org/url/github.com/ipython/ipython/raw/master/examples/notebooks/Part%205%20-%20Rich%20Display%20System.ipynb" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/latex": [ | |
| "\\begin{aligned}\n", | |
| "\\nabla \\times \\vec{\\mathbf{B}} -\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{E}}}{\\partial t} & = \\frac{4\\pi}{c}\\vec{\\mathbf{j}} \\\\\n", | |
| "\\nabla \\cdot \\vec{\\mathbf{E}} & = 4 \\pi \\rho \\\\\n", | |
| "\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n", | |
| "\\nabla \\cdot \\vec{\\mathbf{B}} & = 0\n", | |
| "\\end{aligned}" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.Latex object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "%%latex\n", | |
| "\\begin{aligned}\n", | |
| "\\nabla \\times \\vec{\\mathbf{B}} -\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{E}}}{\\partial t} & = \\frac{4\\pi}{c}\\vec{\\mathbf{j}} \\\\\n", | |
| "\\nabla \\cdot \\vec{\\mathbf{E}} & = 4 \\pi \\rho \\\\\n", | |
| "\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n", | |
| "\\nabla \\cdot \\vec{\\mathbf{B}} & = 0\n", | |
| "\\end{aligned}" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/latex": [ | |
| "\\begin{tabular}{ | c | c c c | } \\hline\n", | |
| " $k$ & $x_1^k$ & $x_2^k$ & $x_3^k$ \\\\\n", | |
| " \\hline\n", | |
| " 0 & -0.30000000 & 0.60000000 & 0.70000000 \\\\\n", | |
| " 1 & 0.47102965 & 0.04883157 & -0.53345964 \\\\\n", | |
| " 2 & 0.49988691 & 0.00228830 & -0.52246185 \\\\\n", | |
| " 3 & 0.49999976 & 0.00005380 & -0.52365600 \\\\\n", | |
| " 4 & 0.50000000 & 0.00000307 & -0.52359743 \\\\\n", | |
| " 5 & 0.50000000 & 0.00000007 & -0.52359885 \\\\\n", | |
| " 6 & 0.50000000 & 0.00000000 & -0.52359877 \\\\\n", | |
| " 7 & 0.50000000 & 0.00000000 & -0.52359878 \\\\\n", | |
| " \\hline\n", | |
| "\\end{tabular}}" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.Latex object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "%%latex\n", | |
| "\\begin{tabular}{ | c | c c c | } \\hline\n", | |
| " $k$ & $x_1^k$ & $x_2^k$ & $x_3^k$ \\\\\n", | |
| " \\hline\n", | |
| " 0 & -0.30000000 & 0.60000000 & 0.70000000 \\\\\n", | |
| " 1 & 0.47102965 & 0.04883157 & -0.53345964 \\\\\n", | |
| " 2 & 0.49988691 & 0.00228830 & -0.52246185 \\\\\n", | |
| " 3 & 0.49999976 & 0.00005380 & -0.52365600 \\\\\n", | |
| " 4 & 0.50000000 & 0.00000307 & -0.52359743 \\\\\n", | |
| " 5 & 0.50000000 & 0.00000007 & -0.52359885 \\\\\n", | |
| " 6 & 0.50000000 & 0.00000000 & -0.52359877 \\\\\n", | |
| " 7 & 0.50000000 & 0.00000000 & -0.52359878 \\\\\n", | |
| " \\hline\n", | |
| "\\end{tabular}}" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/latex": [ | |
| "\\documentclass[12pt]{article}\n", | |
| "\n", | |
| "\\setlength{\\parskip}{1.2ex}\t % space between paragraphs\n", | |
| "\\setlength{\\parindent}{2em}\t % amount of indention\n", | |
| "\\setlength{\\textwidth}{175cm}\t % default = 6.5\"\n", | |
| "\\setlength{\\oddsidemargin}{-5mm} % default = 0\"\n", | |
| "\\setlength{\\textheight}{225mm}\t % default = 9\"\n", | |
| "\\setlength{\\topmargin}{-12mm}\t % default = 0\"\n", | |
| "\n", | |
| "\t% --- define your own commands!! ---\n", | |
| "\\newcommand{\\iii}{\\indent \\indent \\indent}\t% triple-depth indent\n", | |
| "\n", | |
| "\\title{A Sample \\LaTeX\\ Document}\n", | |
| "\\author{Schl\\oe ff\\d{o}nffl\\t{oo}\\ae g\\\"{e}n, \\L\\\"{a}rs}\n", | |
| "\\date{July 14, 1992}\n", | |
| "\n", | |
| "\\begin{document}\n", | |
| "\t\t\t\t(PAGE 1)\n", | |
| "\\maketitle\n", | |
| "\n", | |
| "\\noindent\n", | |
| "I{\\footnotesize MPORTANT} S{\\footnotesize TUFF} \\\\\n", | |
| "{\\bf \tI{\\bf \\footnotesize MPORTANT} S{\\bf \\footnotesize TUFF}} \\\\\n", | |
| "\\textbf{ I{\\footnotesize MPORTANT} S{\\footnotesize TUFF}}\n", | |
| "\n", | |
| "This is a document produced by the \\LaTeX\\ software, and generated by the\n", | |
| "source file {\\tt sample.tex}. Compare the source text file (left-hand\n", | |
| "sides) with the document it produces using \\LaTeX\\ (right-hand sides).\n", | |
| "\n", | |
| "\\section{Ordinary Text}\t% Produces section heading. Lower-level sections\n", | |
| "\t\t\t% are begun with similar \\subsection and\n", | |
| "\t\t\t% \\subsubsection commands; numbering is automatic!\n", | |
| "\n", | |
| "\\subsection{Spacing in the source text}\n", | |
| "The ends of words and sentences are marked\n", | |
| " by spaces. It doesn't matter how many\n", | |
| "spaces\n", | |
| "you\n", | |
| "type; one is as good as 100.\n", | |
| "The end of a line counts as a space.\n", | |
| "\n", | |
| "One or more blank lines denote the end of a paragraph.\n", | |
| "\n", | |
| "Since any number of consecutive spaces are treated like a single one, the\n", | |
| "formatting of the input file makes no difference to \\TeX, but it makes a\n", | |
| "difference to you. When you use \\LaTeX, making your input file as easy to\n", | |
| "read as possible will be a great help as you write your document and when\n", | |
| "you change it. Keep typed lines {\\bf short} in length, and use\n", | |
| "\\verb9 % comments9. % like this!\n", | |
| "\n", | |
| "Because printing is different from typewriting, there are a number of things\n", | |
| "that you have to do differently when preparing an input file than if you were\n", | |
| "just typing the document directly. Quotation marks like ``this'' have to\n", | |
| "be handled specially.\n", | |
| "\n", | |
| "\\subsection{Special characters}\n", | |
| "Dashes come in three sizes: an\n", | |
| " intra-word\n", | |
| "dash, a medium dash for number ranges like\n", | |
| " 1--2,\n", | |
| "and a punctuation\n", | |
| " dash---like\n", | |
| "this.\n", | |
| "\n", | |
| "\\TeX\\ interprets some common characters as commands, so you must type\n", | |
| "special commands to generate them. These characters include the\n", | |
| "following: \\$ \\& \\% \\# \\{ and \\}.\n", | |
| "\n", | |
| "\\subsection{Fonts}\t\t(PAGE 2)\n", | |
| "In printing, text is emphasized by using an {\\em italic\\/}\n", | |
| "type style. % The \\/ command produces the tiny extra space that\n", | |
| " % should be added between a slanted and a following\n", | |
| " % unslanted letter.\n", | |
| "\\begin{em}\n", | |
| " A long segment of text can also be emphasized in this way. Text within\n", | |
| " such a segment given additional emphasis\n", | |
| " with\\/ {\\em Roman}\n", | |
| " type. Italic type loses its ability to emphasize and become simply\n", | |
| " distracting when used excessively.\n", | |
| "\\end{em}\n", | |
| "\n", | |
| "Other font types are available: \\\\\n", | |
| "\\indent {\\bf Bold face type,}\t\\\\\n", | |
| "\\indent {\\tt typewriter style type,}\t\\\\\n", | |
| "\\indent {\\sf sans-serif type,}\t\\\\\n", | |
| "\\indent {\\sl slanted type,}\t\\\\\n", | |
| "\\indent {\\sc all caps type.}\t\\\\\n", | |
| "Formulae and other mathematical expressions are given\n", | |
| "their own ``math mode'' font.\n", | |
| "\n", | |
| "\\section{Spacing}\n", | |
| "A sentence-ending space should be larger than the space between words\n", | |
| "within a sentence. You sometimes have to type special commands in\n", | |
| "conjunction with punctuation characters to get this right, as in the\n", | |
| "following sentence.\n", | |
| " Gnats, gnus, etc.\\ % `\\ ' makes an inter-word space.\n", | |
| " all begin with G\\@. % \\@ marks end-of-sentence punctuation.\n", | |
| "Generating an ellipsis\n", | |
| " \\ldots\\\t% `\\ ' needed because TeX ignores spaces after\n", | |
| "\t\t% command names like \\ldots made from \\ + letters.\n", | |
| "with the right spacing around the periods requires a special command.\n", | |
| "\n", | |
| "It is sometimes necessary to prevent \\TeX\\ from breaking a line where\n", | |
| "it might otherwise do so. This may be at a space, as between the\n", | |
| "``Mr.'' and ``Jones'' in\n", | |
| "``Mr.~Jones'', %\t~ produces an unbreakable interword space.\n", | |
| "or within a word---especially when the word is a symbol like\n", | |
| "\\mbox{\\em itemnum\\/} that makes little sense when hyphenated\n", | |
| "across lines.\n", | |
| "\n", | |
| "In math mode, \\TeX\\ ignores the spaces you type and formats\n", | |
| "the formula the way it thinks is best. Some authors feel that\n", | |
| "\\TeX\\ cramps formulae, and they want to add more space; however,\n", | |
| "\\TeX\\ knows more about typesetting formulae than do many authors.\n", | |
| "Adding extra space usually makes a formula prettier but\n", | |
| "harder to read, because it visually fractures the formula into\n", | |
| "separate units.\n", | |
| "\n", | |
| "Though fiddling with the spacing is dangerous, you sometimes\n", | |
| "have to do it to make a formula look just right. One reason\n", | |
| "is that \\TeX\\ may not understand the formula's logical structure,\n", | |
| "interpreting (for example) ${\\bf y\\:dx}$ as the product of\n", | |
| "three quantities rather than as $y$ times the differential $dx$,\n", | |
| "so that it doesn't add the little extra space after the $y$.\n", | |
| "You can define your own commands to take care of such cases,\n", | |
| "or use these special spacing commands:\t\\\\\n", | |
| "\\iii \\verb2\\,2~~~thin space~~~~~~(any mode) \\\\\t\t% \"verbatim\"\n", | |
| "\\iii \\verb9\\:9~~~medium space~~~~(math mode only) \\\\\n", | |
| "\\iii \\verb#\\;#~~~thick space~~~~~(math mode only) \\\\\n", | |
| "\\iii \\verb2\\!2~~~thin backspace~~(math mode only) \\\\\n", | |
| "A most precise spacing command can be used in either math or\n", | |
| "paragraph modes; the \\verb2\\kern2 command. Use it with the\n", | |
| "unit ``em'', which is the width of a capital M. Example:\n", | |
| "to print `R' over an `I' you might use the command\n", | |
| "\\verb@I\\kern-0.27emR@ to produce ``I\\kern-0.27emR''.\n", | |
| "\n", | |
| "\\section{Displayed Text}\t\t(PAGE 3)\n", | |
| "Text is displayed by indenting it from the left margin.\n", | |
| "Quotations are commonly displayed. There are short quotations\n", | |
| "\\begin{quote}\n", | |
| " This is a short a quotation. It consists of a\n", | |
| " single paragraph of text. There is no paragraph\n", | |
| " indentation.\n", | |
| "\\end{quote}\n", | |
| "and longer ones.\n", | |
| "\\begin{quotation}\n", | |
| " This is a longer quotation. It consists of two paragraphs\n", | |
| " of text. The beginning of each paragraph is indicated\n", | |
| " by an extra indentation.\n", | |
| "\n", | |
| " This is the second paragraph of the quotation. It is just\n", | |
| " as dull as the first paragraph.\n", | |
| "\\end{quotation}\n", | |
| "\n", | |
| "Footnotes\\footnote{This is an example of a footnote.} pose no problem.\n", | |
| "Likewise, bibliographic references \\cite{Lam} are handled with ease.\n", | |
| "!`\\TeX\\ can g\\`{e}n\\'{e}rate alm\\\"{o}st all the accents and\n", | |
| "spe\\c{c}ial symbols used in Western \\cite{Sch} l\\aa nguages! Likewise,\n", | |
| "its arsenal of mathematical sym$\\beta$ols, introduced below, is formidable.\n", | |
| "\n", | |
| "Another frequently-displayed structure is a list.\n", | |
| "The following is an example of an {\\em itemized} list.\n", | |
| " \\begin{itemize}\n", | |
| " \\item This is the first item of an itemized list. Each item\n", | |
| " in the list is marked with a ``tick''. The document\n", | |
| " style determines what kind of tick mark is used.\n", | |
| "\n", | |
| " \\item This is the second item of the list. Need there be more?\n", | |
| " \\end{itemize}\n", | |
| "\n", | |
| "\\section{Mathematical Formulae}\n", | |
| "\\TeX\\ is good at typesetting mathematical formulas like\n", | |
| " $ x-3y = 7 $\n", | |
| "or\n", | |
| " $ y_{i+1} = x_{i}^{2n} - \\sqrt{5}x_{i}^{n} + 1$.\n", | |
| "Remember that a letter like\n", | |
| " \\( x \\) % $ ... $ and \\( ... \\) are equivalent\n", | |
| "is a formula when it denotes a mathematical symbol, and should\n", | |
| "be treated as one.\n", | |
| "\n", | |
| "Mathematical formulas may also be\t\t% use \\[ \\]\n", | |
| "{\\em displayed}. A displayed formula\t\t% or $$ $$\n", | |
| "is one-line long; multiline formulas\t\t% or \\begin{equation}\n", | |
| "require special formatting instructions.\t% \\begin{eqnarray}\n", | |
| "The following formulae demonstrate\n", | |
| "many constructions you might find useful.\n", | |
| "Refer to equation (\\ref{eq:fermat}), which is probably true,\n", | |
| "while equations (\\ref{eq:dumb}-\\ref{eq:realdumb}) are silly.\n", | |
| "Note that the \\verb9equation9 and \\verb9eqnarray9 environments\n", | |
| "number the equations, but \\verb9eqnarray*9 doesn't.\n", | |
| "\\[ x_{i+1} ~=~ N^{i+1}(x_{0}) ~=~ N(x_{i}) ~=~\n", | |
| "\tx_{i} - \\frac{f(x_{i})}{f'(x_{i})}\t\\]\n", | |
| "\n", | |
| "$$ \\frac{\\partial u}{\\partial t} + \\nabla^{4}u + \\nabla^{2}u +\n", | |
| "\t\\frac12 |\\nabla u|^{2}~ =~ c^2 $$\n", | |
| "\n", | |
| "\t\t\t\t(PAGE 4)\n", | |
| "\\begin{equation} a^{p} + b^p \\neq c^{p} ~~~\\mbox{for } p>2\n", | |
| "\t~~ \\mbox{(see proof in margin)} \\label{eq:fermat}\n", | |
| "\\end{equation}\n", | |
| "$$ \\lim_{n \\rightarrow \\infty}x_{n} \\geq \\pi $$\n", | |
| "$$ \\forall x \\in {\\cal O} ~~\\exists \\delta ~~~\\mbox{such that}~~~\n", | |
| "\t|y-x|<\\delta ~\\Rightarrow ~y \\in {\\cal O} $$\n", | |
| "\\vspace{4mm}\n", | |
| "$$\n", | |
| "\\Psi' = \\frac{d}{d \\phi} \\left( \\begin{array}{c}\n", | |
| " \\phi_{2} \\\\ \\phi_{3} \\\\ 1 - \\phi_{2} - \\phi_{1}^{2}/2\n", | |
| " \\end{array} \\right)\n", | |
| " ~~~~~~~~~~~~~\n", | |
| " \\Theta = \\left(\t\\begin{array}{ccc}\n", | |
| "\t0 \t\t\t& \t1\t&\t0\t\\\\\n", | |
| "- \\theta_{1} \\psi_{1} - \\psi_{2} &\t0\t&\t\\psi_3\t\\\\\n", | |
| "\t-\\phi_{1} \t\t&\t-1\t&\t0\n", | |
| "\t\t\t\\end{array} \\right)\n", | |
| "$$\n", | |
| "\\vspace{4mm}\n", | |
| "\\begin{eqnarray}\n", | |
| "\t\\int_0^{\\infty} e^{-x^2}\\,dx\n", | |
| "\t& = &\te^{-\\left(\\int_0^{\\infty}x\\,dx\\right)^2} \\label{eq:dumb} \\\\\n", | |
| "\t& = &\te^{-\\infty} ~~~~~\\mbox{(bogus)} \\\\\n", | |
| "\t& = &\t0.38-1.7i ~~~~~\\mbox{(not!)} \\label{eq:realdumb}\n", | |
| "\\end{eqnarray}\n", | |
| "\\vspace{4mm}\n", | |
| "\\begin{eqnarray*}\t\t\t% \"*\" = no line numbering\n", | |
| " \\sum_{n=1}^k \\frac1n\n", | |
| "\t& \\approx &\t\\ln k + \\gamma \\\\\n", | |
| "\t& = &\t\t(\\ln 10)(\\log_{10}k) + \\gamma \\\\\n", | |
| "\t& \\approx &\t2.3026\\log_{10}k + 0.57772\n", | |
| "\\end{eqnarray*}\n", | |
| "\n", | |
| "\\vspace{6mm}\n", | |
| "\\centerline{\n", | |
| "\\begin{tabular}{ | c | c c c | } \\hline\n", | |
| " $k$ & $x_1^k$ & $x_2^k$ & $x_3^k$ \\\\\n", | |
| " \\hline\n", | |
| " 0 & -0.30000000 & 0.60000000 & 0.70000000 \\\\\n", | |
| " 1 & 0.47102965 & 0.04883157 & -0.53345964 \\\\\n", | |
| " 2 & 0.49988691 & 0.00228830 & -0.52246185 \\\\\n", | |
| " 3 & 0.49999976 & 0.00005380 & -0.52365600 \\\\\n", | |
| " 4 & 0.50000000 & 0.00000307 & -0.52359743 \\\\\n", | |
| " 5 & 0.50000000 & 0.00000007 & -0.52359885 \\\\\n", | |
| " 6 & 0.50000000 & 0.00000000 & -0.52359877 \\\\\n", | |
| " 7 & 0.50000000 & 0.00000000 & -0.52359878 \\\\\n", | |
| " \\hline\n", | |
| "\\end{tabular}}\n", | |
| "\n", | |
| "Unary operators ``plus'' and ``minus'' -- just use exponentiation:\n", | |
| "$$\t{}^{+}0.168 \\mbox{ or } {}^{-}1.168\t$$\n", | |
| "\n", | |
| "$$ \\Vert \\diamond\\star \\Vert ~~~ \\clubsuit\\diamondsuit\\heartsuit\\spadesuit\n", | |
| " ~~~ \\sharp\\flat\\natural ~~~ \\cap\\cup\\pm\\mp ~~~ \\prod\\alpha\\beta\\gamma\n", | |
| " ~~~ \\oint_Cf(z)dz ~~~ \\Gamma_{\\sqrt7}^{v,\\upsilon} ~~~ V\\bigoplus W $$\n", | |
| "\n", | |
| "\t\t\t\t(PAGE 5)\n", | |
| "\\begin{thebibliography}{9}\t% 9 = maximum expected references!\n", | |
| "\n", | |
| "\\bibitem{Lam} Lamport, Leslie.\n", | |
| "\\LaTeX : A Document Preparation System. \\\\\n", | |
| "Copyright \\copyright 1986, Addison-Wesley Publ.Co.,Inc.\n", | |
| "\n", | |
| "\\bibitem{Sch} Schl\\oe ff\\d{o}nffl\\t{oo}\\ae g\\\"{e}n,\n", | |
| "\\L\\\"{a}rs. Silly Typography.\t\t\\\\\n", | |
| "{\\em Journal of Linguistic Horseplay 19D} (1977), 23-37.\n", | |
| "\n", | |
| "\\end{thebibliography}\n", | |
| "\\end{document} % End of document." | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.Latex object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "%%latex\n", | |
| "\\documentclass[12pt]{article}\n", | |
| "\n", | |
| "\\setlength{\\parskip}{1.2ex}\t % space between paragraphs\n", | |
| "\\setlength{\\parindent}{2em}\t % amount of indention\n", | |
| "\\setlength{\\textwidth}{175cm}\t % default = 6.5\"\n", | |
| "\\setlength{\\oddsidemargin}{-5mm} % default = 0\"\n", | |
| "\\setlength{\\textheight}{225mm}\t % default = 9\"\n", | |
| "\\setlength{\\topmargin}{-12mm}\t % default = 0\"\n", | |
| "\n", | |
| "\t% --- define your own commands!! ---\n", | |
| "\\newcommand{\\iii}{\\indent \\indent \\indent}\t% triple-depth indent\n", | |
| "\n", | |
| "\\title{A Sample \\LaTeX\\ Document}\n", | |
| "\\author{Schl\\oe ff\\d{o}nffl\\t{oo}\\ae g\\\"{e}n, \\L\\\"{a}rs}\n", | |
| "\\date{July 14, 1992}\n", | |
| "\n", | |
| "\\begin{document}\n", | |
| "\t\t\t\t(PAGE 1)\n", | |
| "\\maketitle\n", | |
| "\n", | |
| "\\noindent\n", | |
| "I{\\footnotesize MPORTANT} S{\\footnotesize TUFF} \\\\\n", | |
| "{\\bf \tI{\\bf \\footnotesize MPORTANT} S{\\bf \\footnotesize TUFF}} \\\\\n", | |
| "\\textbf{ I{\\footnotesize MPORTANT} S{\\footnotesize TUFF}}\n", | |
| "\n", | |
| "This is a document produced by the \\LaTeX\\ software, and generated by the\n", | |
| "source file {\\tt sample.tex}. Compare the source text file (left-hand\n", | |
| "sides) with the document it produces using \\LaTeX\\ (right-hand sides).\n", | |
| "\n", | |
| "\\section{Ordinary Text}\t% Produces section heading. Lower-level sections\n", | |
| "\t\t\t% are begun with similar \\subsection and\n", | |
| "\t\t\t% \\subsubsection commands; numbering is automatic!\n", | |
| "\n", | |
| "\\subsection{Spacing in the source text}\n", | |
| "The ends of words and sentences are marked\n", | |
| " by spaces. It doesn't matter how many\n", | |
| "spaces\n", | |
| "you\n", | |
| "type; one is as good as 100.\n", | |
| "The end of a line counts as a space.\n", | |
| "\n", | |
| "One or more blank lines denote the end of a paragraph.\n", | |
| "\n", | |
| "Since any number of consecutive spaces are treated like a single one, the\n", | |
| "formatting of the input file makes no difference to \\TeX, but it makes a\n", | |
| "difference to you. When you use \\LaTeX, making your input file as easy to\n", | |
| "read as possible will be a great help as you write your document and when\n", | |
| "you change it. Keep typed lines {\\bf short} in length, and use\n", | |
| "\\verb9 % comments9. % like this!\n", | |
| "\n", | |
| "Because printing is different from typewriting, there are a number of things\n", | |
| "that you have to do differently when preparing an input file than if you were\n", | |
| "just typing the document directly. Quotation marks like ``this'' have to\n", | |
| "be handled specially.\n", | |
| "\n", | |
| "\\subsection{Special characters}\n", | |
| "Dashes come in three sizes: an\n", | |
| " intra-word\n", | |
| "dash, a medium dash for number ranges like\n", | |
| " 1--2,\n", | |
| "and a punctuation\n", | |
| " dash---like\n", | |
| "this.\n", | |
| "\n", | |
| "\\TeX\\ interprets some common characters as commands, so you must type\n", | |
| "special commands to generate them. These characters include the\n", | |
| "following: \\$ \\& \\% \\# \\{ and \\}.\n", | |
| "\n", | |
| "\\subsection{Fonts}\t\t(PAGE 2)\n", | |
| "In printing, text is emphasized by using an {\\em italic\\/}\n", | |
| "type style. % The \\/ command produces the tiny extra space that\n", | |
| " % should be added between a slanted and a following\n", | |
| " % unslanted letter.\n", | |
| "\\begin{em}\n", | |
| " A long segment of text can also be emphasized in this way. Text within\n", | |
| " such a segment given additional emphasis\n", | |
| " with\\/ {\\em Roman}\n", | |
| " type. Italic type loses its ability to emphasize and become simply\n", | |
| " distracting when used excessively.\n", | |
| "\\end{em}\n", | |
| "\n", | |
| "Other font types are available: \\\\\n", | |
| "\\indent {\\bf Bold face type,}\t\\\\\n", | |
| "\\indent {\\tt typewriter style type,}\t\\\\\n", | |
| "\\indent {\\sf sans-serif type,}\t\\\\\n", | |
| "\\indent {\\sl slanted type,}\t\\\\\n", | |
| "\\indent {\\sc all caps type.}\t\\\\\n", | |
| "Formulae and other mathematical expressions are given\n", | |
| "their own ``math mode'' font.\n", | |
| "\n", | |
| "\\section{Spacing}\n", | |
| "A sentence-ending space should be larger than the space between words\n", | |
| "within a sentence. You sometimes have to type special commands in\n", | |
| "conjunction with punctuation characters to get this right, as in the\n", | |
| "following sentence.\n", | |
| " Gnats, gnus, etc.\\ % `\\ ' makes an inter-word space.\n", | |
| " all begin with G\\@. % \\@ marks end-of-sentence punctuation.\n", | |
| "Generating an ellipsis\n", | |
| " \\ldots\\\t% `\\ ' needed because TeX ignores spaces after\n", | |
| "\t\t% command names like \\ldots made from \\ + letters.\n", | |
| "with the right spacing around the periods requires a special command.\n", | |
| "\n", | |
| "It is sometimes necessary to prevent \\TeX\\ from breaking a line where\n", | |
| "it might otherwise do so. This may be at a space, as between the\n", | |
| "``Mr.'' and ``Jones'' in\n", | |
| "``Mr.~Jones'', %\t~ produces an unbreakable interword space.\n", | |
| "or within a word---especially when the word is a symbol like\n", | |
| "\\mbox{\\em itemnum\\/} that makes little sense when hyphenated\n", | |
| "across lines.\n", | |
| "\n", | |
| "In math mode, \\TeX\\ ignores the spaces you type and formats\n", | |
| "the formula the way it thinks is best. Some authors feel that\n", | |
| "\\TeX\\ cramps formulae, and they want to add more space; however,\n", | |
| "\\TeX\\ knows more about typesetting formulae than do many authors.\n", | |
| "Adding extra space usually makes a formula prettier but\n", | |
| "harder to read, because it visually fractures the formula into\n", | |
| "separate units.\n", | |
| "\n", | |
| "Though fiddling with the spacing is dangerous, you sometimes\n", | |
| "have to do it to make a formula look just right. One reason\n", | |
| "is that \\TeX\\ may not understand the formula's logical structure,\n", | |
| "interpreting (for example) ${\\bf y\\:dx}$ as the product of\n", | |
| "three quantities rather than as $y$ times the differential $dx$,\n", | |
| "so that it doesn't add the little extra space after the $y$.\n", | |
| "You can define your own commands to take care of such cases,\n", | |
| "or use these special spacing commands:\t\\\\\n", | |
| "\\iii \\verb2\\,2~~~thin space~~~~~~(any mode) \\\\\t\t% \"verbatim\"\n", | |
| "\\iii \\verb9\\:9~~~medium space~~~~(math mode only) \\\\\n", | |
| "\\iii \\verb#\\;#~~~thick space~~~~~(math mode only) \\\\\n", | |
| "\\iii \\verb2\\!2~~~thin backspace~~(math mode only) \\\\\n", | |
| "A most precise spacing command can be used in either math or\n", | |
| "paragraph modes; the \\verb2\\kern2 command. Use it with the\n", | |
| "unit ``em'', which is the width of a capital M. Example:\n", | |
| "to print `R' over an `I' you might use the command\n", | |
| "\\verb@I\\kern-0.27emR@ to produce ``I\\kern-0.27emR''.\n", | |
| "\n", | |
| "\\section{Displayed Text}\t\t(PAGE 3)\n", | |
| "Text is displayed by indenting it from the left margin.\n", | |
| "Quotations are commonly displayed. There are short quotations\n", | |
| "\\begin{quote}\n", | |
| " This is a short a quotation. It consists of a\n", | |
| " single paragraph of text. There is no paragraph\n", | |
| " indentation.\n", | |
| "\\end{quote}\n", | |
| "and longer ones.\n", | |
| "\\begin{quotation}\n", | |
| " This is a longer quotation. It consists of two paragraphs\n", | |
| " of text. The beginning of each paragraph is indicated\n", | |
| " by an extra indentation.\n", | |
| "\n", | |
| " This is the second paragraph of the quotation. It is just\n", | |
| " as dull as the first paragraph.\n", | |
| "\\end{quotation}\n", | |
| "\n", | |
| "Footnotes\\footnote{This is an example of a footnote.} pose no problem.\n", | |
| "Likewise, bibliographic references \\cite{Lam} are handled with ease.\n", | |
| "!`\\TeX\\ can g\\`{e}n\\'{e}rate alm\\\"{o}st all the accents and\n", | |
| "spe\\c{c}ial symbols used in Western \\cite{Sch} l\\aa nguages! Likewise,\n", | |
| "its arsenal of mathematical sym$\\beta$ols, introduced below, is formidable.\n", | |
| "\n", | |
| "Another frequently-displayed structure is a list.\n", | |
| "The following is an example of an {\\em itemized} list.\n", | |
| " \\begin{itemize}\n", | |
| " \\item This is the first item of an itemized list. Each item\n", | |
| " in the list is marked with a ``tick''. The document\n", | |
| " style determines what kind of tick mark is used.\n", | |
| "\n", | |
| " \\item This is the second item of the list. Need there be more?\n", | |
| " \\end{itemize}\n", | |
| "\n", | |
| "\\section{Mathematical Formulae}\n", | |
| "\\TeX\\ is good at typesetting mathematical formulas like\n", | |
| " $ x-3y = 7 $\n", | |
| "or\n", | |
| " $ y_{i+1} = x_{i}^{2n} - \\sqrt{5}x_{i}^{n} + 1$.\n", | |
| "Remember that a letter like\n", | |
| " \\( x \\) % $ ... $ and \\( ... \\) are equivalent\n", | |
| "is a formula when it denotes a mathematical symbol, and should\n", | |
| "be treated as one.\n", | |
| "\n", | |
| "Mathematical formulas may also be\t\t% use \\[ \\]\n", | |
| "{\\em displayed}. A displayed formula\t\t% or $$ $$\n", | |
| "is one-line long; multiline formulas\t\t% or \\begin{equation}\n", | |
| "require special formatting instructions.\t% \\begin{eqnarray}\n", | |
| "The following formulae demonstrate\n", | |
| "many constructions you might find useful.\n", | |
| "Refer to equation (\\ref{eq:fermat}), which is probably true,\n", | |
| "while equations (\\ref{eq:dumb}-\\ref{eq:realdumb}) are silly.\n", | |
| "Note that the \\verb9equation9 and \\verb9eqnarray9 environments\n", | |
| "number the equations, but \\verb9eqnarray*9 doesn't.\n", | |
| "\\[ x_{i+1} ~=~ N^{i+1}(x_{0}) ~=~ N(x_{i}) ~=~\n", | |
| "\tx_{i} - \\frac{f(x_{i})}{f'(x_{i})}\t\\]\n", | |
| "\n", | |
| "$$ \\frac{\\partial u}{\\partial t} + \\nabla^{4}u + \\nabla^{2}u +\n", | |
| "\t\\frac12 |\\nabla u|^{2}~ =~ c^2 $$\n", | |
| "\n", | |
| "\t\t\t\t(PAGE 4)\n", | |
| "\\begin{equation} a^{p} + b^p \\neq c^{p} ~~~\\mbox{for } p>2\n", | |
| "\t~~ \\mbox{(see proof in margin)} \\label{eq:fermat}\n", | |
| "\\end{equation}\n", | |
| "$$ \\lim_{n \\rightarrow \\infty}x_{n} \\geq \\pi $$\n", | |
| "$$ \\forall x \\in {\\cal O} ~~\\exists \\delta ~~~\\mbox{such that}~~~\n", | |
| "\t|y-x|<\\delta ~\\Rightarrow ~y \\in {\\cal O} $$\n", | |
| "\\vspace{4mm}\n", | |
| "$$\n", | |
| "\\Psi' = \\frac{d}{d \\phi} \\left( \\begin{array}{c}\n", | |
| " \\phi_{2} \\\\ \\phi_{3} \\\\ 1 - \\phi_{2} - \\phi_{1}^{2}/2\n", | |
| " \\end{array} \\right)\n", | |
| " ~~~~~~~~~~~~~\n", | |
| " \\Theta = \\left(\t\\begin{array}{ccc}\n", | |
| "\t0 \t\t\t& \t1\t&\t0\t\\\\\n", | |
| "- \\theta_{1} \\psi_{1} - \\psi_{2} &\t0\t&\t\\psi_3\t\\\\\n", | |
| "\t-\\phi_{1} \t\t&\t-1\t&\t0\n", | |
| "\t\t\t\\end{array} \\right)\n", | |
| "$$\n", | |
| "\\vspace{4mm}\n", | |
| "\\begin{eqnarray}\n", | |
| "\t\\int_0^{\\infty} e^{-x^2}\\,dx\n", | |
| "\t& = &\te^{-\\left(\\int_0^{\\infty}x\\,dx\\right)^2} \\label{eq:dumb} \\\\\n", | |
| "\t& = &\te^{-\\infty} ~~~~~\\mbox{(bogus)} \\\\\n", | |
| "\t& = &\t0.38-1.7i ~~~~~\\mbox{(not!)} \\label{eq:realdumb}\n", | |
| "\\end{eqnarray}\n", | |
| "\\vspace{4mm}\n", | |
| "\\begin{eqnarray*}\t\t\t% \"*\" = no line numbering\n", | |
| " \\sum_{n=1}^k \\frac1n\n", | |
| "\t& \\approx &\t\\ln k + \\gamma \\\\\n", | |
| "\t& = &\t\t(\\ln 10)(\\log_{10}k) + \\gamma \\\\\n", | |
| "\t& \\approx &\t2.3026\\log_{10}k + 0.57772\n", | |
| "\\end{eqnarray*}\n", | |
| "\n", | |
| "\\vspace{6mm}\n", | |
| "\\centerline{\n", | |
| "\\begin{tabular}{ | c | c c c | } \\hline\n", | |
| " $k$ & $x_1^k$ & $x_2^k$ & $x_3^k$ \\\\\n", | |
| " \\hline\n", | |
| " 0 & -0.30000000 & 0.60000000 & 0.70000000 \\\\\n", | |
| " 1 & 0.47102965 & 0.04883157 & -0.53345964 \\\\\n", | |
| " 2 & 0.49988691 & 0.00228830 & -0.52246185 \\\\\n", | |
| " 3 & 0.49999976 & 0.00005380 & -0.52365600 \\\\\n", | |
| " 4 & 0.50000000 & 0.00000307 & -0.52359743 \\\\\n", | |
| " 5 & 0.50000000 & 0.00000007 & -0.52359885 \\\\\n", | |
| " 6 & 0.50000000 & 0.00000000 & -0.52359877 \\\\\n", | |
| " 7 & 0.50000000 & 0.00000000 & -0.52359878 \\\\\n", | |
| " \\hline\n", | |
| "\\end{tabular}}\n", | |
| "\n", | |
| "Unary operators ``plus'' and ``minus'' -- just use exponentiation:\n", | |
| "$$\t{}^{+}0.168 \\mbox{ or } {}^{-}1.168\t$$\n", | |
| "\n", | |
| "$$ \\Vert \\diamond\\star \\Vert ~~~ \\clubsuit\\diamondsuit\\heartsuit\\spadesuit\n", | |
| " ~~~ \\sharp\\flat\\natural ~~~ \\cap\\cup\\pm\\mp ~~~ \\prod\\alpha\\beta\\gamma\n", | |
| " ~~~ \\oint_Cf(z)dz ~~~ \\Gamma_{\\sqrt7}^{v,\\upsilon} ~~~ V\\bigoplus W $$\n", | |
| "\n", | |
| "\t\t\t\t(PAGE 5)\n", | |
| "\\begin{thebibliography}{9}\t% 9 = maximum expected references!\n", | |
| "\n", | |
| "\\bibitem{Lam} Lamport, Leslie.\n", | |
| "\\LaTeX : A Document Preparation System. \\\\\n", | |
| "Copyright \\copyright 1986, Addison-Wesley Publ.Co.,Inc.\n", | |
| "\n", | |
| "\\bibitem{Sch} Schl\\oe ff\\d{o}nffl\\t{oo}\\ae g\\\"{e}n,\n", | |
| "\\L\\\"{a}rs. Silly Typography.\t\t\\\\\n", | |
| "{\\em Journal of Linguistic Horseplay 19D} (1977), 23-37.\n", | |
| "\n", | |
| "\\end{thebibliography}\n", | |
| "\\end{document} % End of document." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "ename": "SyntaxError", | |
| "evalue": "invalid syntax (<ipython-input-6-014c9c395e7a>, line 1)", | |
| "output_type": "error", | |
| "traceback": [ | |
| "\u001b[0;36m File \u001b[0;32m\"<ipython-input-6-014c9c395e7a>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m from http://spot.colorado.edu/~sitelic/samplecode/latex/AiryBessel.html\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "from http://spot.colorado.edu/~sitelic/samplecode/latex/AiryBessel.html " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/latex": [ | |
| "\n", | |
| "$$\n", | |
| "\\frac{1}{3}\\\n", | |
| "$$\n", | |
| "\n", | |
| "$$\n", | |
| "\\frac{obs}{expe}\\\n", | |
| "$$\n", | |
| "\n", | |
| "$$ Ai(z) =\n", | |
| "\t\\frac13\\sqrt{z}\\left[\n", | |
| "\tI_{-1/3}(\\zeta)\n", | |
| "\t-I_{1/3}(\\zeta) \\right]\n", | |
| "\t=\n", | |
| "\t\\pi^{-1}\\sqrt{z/3}K_{1/3}(\\zeta)\n", | |
| "$$\n", | |
| "\n", | |
| "{\\bf 10.4.15}\n", | |
| "$$ Ai(-z) =\n", | |
| "\t\\frac13\\sqrt{z}\n", | |
| "\t\\left[\n", | |
| "\tJ_{1/3}(\\zeta) +\n", | |
| "\tJ_{-1/3}(\\zeta) \\right]\n", | |
| "\t=\n", | |
| "\t\\frac12 \\sqrt{z/3} \\left[\n", | |
| "\te^{\\pi i/6} H_{1/3}^{(1)}(\\zeta)\n", | |
| "\t+ e^{-\\pi i/6}H_{1/3}^{(2)}(\\zeta)\n", | |
| "\t\\right]\n", | |
| "$$" | |
| ], | |
| "text/plain": [ | |
| "<IPython.core.display.Latex object>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "%%latex\n", | |
| "\n", | |
| "$$\n", | |
| "\\frac{1}{3}\\\n", | |
| "$$\n", | |
| "\n", | |
| "$$\n", | |
| "\\frac{obs}{expe}\\\n", | |
| "$$\n", | |
| "\n", | |
| "$$ Ai(z) =\n", | |
| "\t\\frac13\\sqrt{z}\\left[\n", | |
| "\tI_{-1/3}(\\zeta)\n", | |
| "\t-I_{1/3}(\\zeta) \\right]\n", | |
| "\t=\n", | |
| "\t\\pi^{-1}\\sqrt{z/3}K_{1/3}(\\zeta)\n", | |
| "$$\n", | |
| "\n", | |
| "{\\bf 10.4.15}\n", | |
| "$$ Ai(-z) =\n", | |
| "\t\\frac13\\sqrt{z}\n", | |
| "\t\\left[\n", | |
| "\tJ_{1/3}(\\zeta) +\n", | |
| "\tJ_{-1/3}(\\zeta) \\right]\n", | |
| "\t=\n", | |
| "\t\\frac12 \\sqrt{z/3} \\left[\n", | |
| "\te^{\\pi i/6} H_{1/3}^{(1)}(\\zeta)\n", | |
| "\t+ e^{-\\pi i/6}H_{1/3}^{(2)}(\\zeta)\n", | |
| "\t\\right]\n", | |
| "$$\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 3", | |
| "language": "python", | |
| "name": "python3" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.6.4" | |
| }, | |
| "widgets": { | |
| "state": {}, | |
| "version": "1.1.2" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 1 | |
| } |
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