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Diffstat (limited to 'info/examples/Math/09-20-1.ltx')
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diff --git a/info/examples/Math/09-20-1.ltx b/info/examples/Math/09-20-1.ltx index 3642bc9c57..58c393d164 100644 --- a/info/examples/Math/09-20-1.ltx +++ b/info/examples/Math/09-20-1.ltx @@ -1,38 +1,44 @@ %% %% Ein Beispiel der DANTE-Edition %% Mathematiksatz mit LaTeX -%% 2. Auflage -%% -%% Beispiel 09-20-1 auf Seite 208. -%% -%% Copyright (C) 2012 Herbert Voss +%% 3. Auflage +%% Beispiel 09-20-1 auf Seite 201. +%% Copyright (C) 2018 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. -%% %% See http://www.latex-project.org/lppl.txt for details. %% -%% %% ==== % Show page(s) 1 %% %% -\documentclass[]{exaarticle} +\documentclass[10pt]{exaartplain} \pagestyle{empty} -\setlength\textwidth{166.324pt} +\setlength\textwidth{352.81416pt} \AtBeginDocument{\setlength\parindent{0pt}} -\setcounter{equation}{31} -\renewcommand\theequation{9.\arabic{equation}} -\StartShownPreambleCommands -\usepackage{xypic} -\StopShownPreambleCommands +%StartShownPreambleCommands +\usepackage{amsmath,mathastext} \MTDeclareVersion[n]{lmvtt}{T1}{lmvtt}{m}{n} +%StopShownPreambleCommands \begin{document} -\begin{equation} -\xymatrix{% - A\POS[];[d]**\dir{~},[];[dr]**\dir{-} & B & C\\ - D & E\POS[];[l]**\dir{.},[];[r]**\dir{~} - & F\POS[];[dl]**\dir{~}\\ - G & H & I} -\end{equation} +\MTversion{lmvtt} +Let $(X,Y)$ be two functions of a variable $a$. If they obey the differential system $(VI_{\nu,n})$: +\begin{align*} a\frac{d}{da} X &= \nu + X - (1 - X^2)\frac{2n a}{1 - a^2}\frac{aX+Y}{1+a XY} \\ +a\frac{d}{da} Y &= -(\nu+1) Y + (1-Y^2)\frac{2n a}{1 - a^2}\frac{X+aY}{1+a XY} +\end{align*} +then the quantity $q=a\frac{aX+Y}{X+aY}$ satisfies as function of $b=a^2$ the $P_{VI}$ +differential equation: +\begin{equation*} +\begin{split} + \frac{d^2 q}{db^2} = \frac12\left\{\frac1q+\frac1{q-1} + +\frac1{q-b}\right\}\left(\frac{dq}{db}\right)^2 - \left\{\frac1b+\frac1{b-1} + +\frac1{q-b}\right\}\frac{dq}{db}\\+\frac{q(q-1)(q-b)}{b^2(b-1)^2}\left\{\alpha+\frac{\beta + b}{q^2} + \frac{\gamma (b-1)}{(q-1)^2}+\frac{\delta + b(b-1)}{(q-b)^2}\right\} +\end{split} +\end{equation*} +with parameters $(\alpha,\beta,\gamma,\delta) = (\frac{(\nu+n)^2}2, +\frac{-(\nu+n+1)^2}2, \frac{n^2}2, \frac{1 - n^2}2)$. \end{document} |