diff options
Diffstat (limited to 'info/examples/Math/09-20-3.ltx')
-rw-r--r-- | info/examples/Math/09-20-3.ltx | 42 |
1 files changed, 28 insertions, 14 deletions
diff --git a/info/examples/Math/09-20-3.ltx b/info/examples/Math/09-20-3.ltx index 8c79982264..40f7586ae8 100644 --- a/info/examples/Math/09-20-3.ltx +++ b/info/examples/Math/09-20-3.ltx @@ -1,32 +1,46 @@ %% %% Ein Beispiel der DANTE-Edition %% Mathematiksatz mit LaTeX -%% 2. Auflage -%% -%% Beispiel 09-20-3 auf Seite 210. -%% -%% Copyright (C) 2012 Herbert Voss +%% 3. Auflage +%% Beispiel 09-20-3 auf Seite 203. +%% 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{352.81416pt} \AtBeginDocument{\setlength\parindent{0pt}} -\StartShownPreambleCommands -\usepackage{xlop} -\StopShownPreambleCommands +%StartShownPreambleCommands +\usepackage[T1]{fontenc} +\usepackage{libertine,amsmath} \renewcommand\familydefault{\sfdefault} +\usepackage[greek=n,biolinum]{libgreek} \renewcommand\familydefault{\sfdefault} +\usepackage[defaultmathsizes]{mathastext} +%StopShownPreambleCommands \begin{document} -\opmul[displayshiftintermediary=shift]{435}{1001205}\hfill -\opmul[displayshiftintermediary=all]{435}{1001205}\hfill -\opmul[displayshiftintermediary=none]{435}{1001205} +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} |