diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex/glossary/sampleEq.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/glossary/sampleEq.tex | 228 |
1 files changed, 228 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/glossary/sampleEq.tex b/Master/texmf-dist/doc/latex/glossary/sampleEq.tex new file mode 100644 index 00000000000..375874f06c5 --- /dev/null +++ b/Master/texmf-dist/doc/latex/glossary/sampleEq.tex @@ -0,0 +1,228 @@ +%% +%% This is file `sampleEq.tex', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% glossary.dtx (with options: `sampleEq.tex,package') +%% Copyright (C) 2005 Nicola Talbot, all rights reserved. +%% If you modify this file, you must change its name first. +%% You are NOT ALLOWED to distribute this file alone. You are NOT +%% ALLOWED to take money for the distribution or use of either this +%% file or a changed version, except for a nominal charge for copying +%% etc. +%% \CharacterTable +%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +%% Digits \0\1\2\3\4\5\6\7\8\9 +%% Exclamation \! Double quote \" Hash (number) \# +%% Dollar \$ Percent \% Ampersand \& +%% Acute accent \' Left paren \( Right paren \) +%% Asterisk \* Plus \+ Comma \, +%% Minus \- Point \. Solidus \/ +%% Colon \: Semicolon \; Less than \< +%% Equals \= Greater than \> Question mark \? +%% Commercial at \@ Left bracket \[ Backslash \\ +%% Right bracket \] Circumflex \^ Underscore \_ +%% Grave accent \` Left brace \{ Vertical bar \| +%% Right brace \} Tilde \~} +\documentclass[a4paper,12pt]{report} + +\usepackage{amsmath} +\usepackage[header,border=none,cols=3]{glossary} + +\newcommand{\erf}{\operatorname{erf}} +\newcommand{\erfc}{\operatorname{erfc}} + +\renewcommand{\theglossarynum}{\theequation} +\renewcommand{\pagecompositor}{.} + +\renewcommand{\glossaryname}{Index of Special Functions and Notations} + +\renewcommand{\glossaryheader}{\bfseries Notation & +\multicolumn{2}{c}{\bfseries +\begin{tabular}{c}Name of the Function and\\the number of +the formula\end{tabular}}\\} + +\makeglossary + +\begin{document} +\title{A Sample Document Using glossary.sty} +\author{Nicola Talbot} +\maketitle + +\begin{abstract} +This is a sample document illustrating the use of the \textsf{glossary} +package. The functions here have been taken from ``Tables of +Integrals, Series, and Products'' by I.S.~Gradshteyn and I.M~Ryzhik. +The glossary is a list of special functions, so +the equation number has been used rather than the page number. This can be +done by defining \verb|\theglossarynum| to be \verb|\theequation|. +The equation numbers are a composite number made up of the chapter number +and number of equation within the chapter. The two parts of the page +number are separated by a fullstop. The default compositor is +a dash \verb|-|, so it needs to be set to a dot by redefining the command +\verb|\pagecompositor|. (This needs to be done \emph{before} the command +\verb|\makeglossary|.) +\end{abstract} + +\printglossary + +\chapter{Gamma Functions} + +\begin{equation} +\Gamma(z) = \int_{0}^{\infty}e^{-t}t^{z-1}\,dt +\end{equation} +\glossary{name=$\Gamma(z)$,description=Gamma function,sort=Gamma} + +\begin{equation} +\Gamma(x+1) = x\Gamma(x) +\end{equation} +\glossary{name=$\Gamma(z)$,description=Gamma function,sort=Gamma} + +\begin{equation} +\gamma(\alpha, x) = \int_0^x e^{-t}t^{\alpha-1}\,dt +\end{equation} +\glossary{name={$\gamma(\alpha,x)$},description=Incomplete gamma function,sort=gamma} + +\begin{equation} +\Gamma(\alpha, x) = \int_x^\infty e^{-t}t^{\alpha-1}\,dt +\end{equation} +\glossary{name={$\Gamma(\alpha,x)$},description=Incomplete gamma function,sort=Gamma} + +\newpage + +\begin{equation} +\Gamma(\alpha) = \Gamma(\alpha, x) + \gamma(\alpha, x) +\end{equation} +\glossary{name=$\Gamma(z)$,description=Gamma function,sort=Gamma} + +\begin{equation} +\psi(x) = \frac{d}{dx}\ln\Gamma(x) +\end{equation} +\glossary{name=$\psi(x)$,description=Psi function,sort=psi} + +\chapter{Error Functions} + +\begin{equation} +\erf(x) = \frac{2}{\surd\pi}\int_0^x e^{-t^2}\,dt +\end{equation} +\glossary{name=$\erf(x)$,description=Error function,sort=erf} + +\begin{equation} +\erfc(x) = 1 - \erf(x) +\end{equation} +\glossary{name=$\erfc(x)$,description=Complementary error function,sort=erfc} + +\chapter{Beta Function} + +\begin{equation} +B(x,y) = 2\int_0^1 t^{x-1}(1-t^2)^{y-1}\,dt +\end{equation} +\glossary{name={$B(x,y)$},description=Beta function,sort=B} +Alternatively: +\begin{equation} +B(x,y) = 2\int_0^{\frac\pi2}\sin^{2x-1}\phi\cos^{2y-1}\phi\,d\phi +\end{equation} +\glossary{name={$B(x,y)$},description=Beta function,sort=B} + +\begin{equation} +B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} = B(y,x) +\end{equation} +\glossary{name={$B(x,y)$},description=Beta function,sort=B} + +\begin{equation} +B_x(p,q) = \int_0^x t^{p-1}(1-t)^{q-1}\,dt +\end{equation} +\glossary{name={$B_x(p,q)$},description=Incomplete beta function,sort=Bx} + +\chapter{Polynomials} + +\section{Chebyshev's polynomials} + +\begin{equation} +T_n(x) = \cos(n\arccos x) +\end{equation} +\glossary{name=$T_n(x)$,description=Chebyshev's polynomials of the first kind,sort=Tn} + +\begin{equation} +U_n(x) = \frac{\sin[(n+1)\arccos x]}{\sin[\arccos x]} +\end{equation} +\glossary{name=$U_n(x)$,description=Chebyshev's polynomials of the second kind,sort=Un} + +\section{Hermite polynomials} + +\begin{equation} +H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n}(e^{-x^2}) +\end{equation} +\glossary{name=$H_n(x)$,description=Hermite polynomials,sort=Hn} + +\section{Laguerre polynomials} + +\begin{equation} +L_n^{\alpha} (x) = \frac{1}{n!}e^x x^{-\alpha} \frac{d^n}{dx^n}(e^{-x}x^{n+\alpha}) +\end{equation} +\glossary{name=$L_n^\alpha(x)$,description=Laguerre polynomials,sort=Lna} + +\chapter{Bessel Functions} + +Bessel functions $Z_\nu(z)$ are solutions of +\begin{equation} +\frac{d^2Z_\nu}{dz^2} + \frac{1}{z}\,\frac{dZ_\nu}{dz} + +\left( +1-\frac{\nu^2}{z^2}Z_\nu = 0 +\right) +\end{equation} +\glossary{name=$Z_\nu(z)$,description=Bessel functions,sort=Z} + +\chapter{Confluent hypergeometric function} + +\begin{equation} +\Phi(\alpha,\gamma;z) = 1 + \frac{\alpha}{\gamma}\,\frac{z}{1!} ++ \frac{\alpha(\alpha+1)}{\gamma(\gamma+1)}\,\frac{z^2}{2!} ++\frac{\alpha(\alpha+1)(\alpha+2)}{\gamma(\gamma+1)(\gamma+2)}\,\frac{z^3}{3!} ++ \cdots +\end{equation} +\glossary{name={$\Phi(\alpha,\gamma;z)$},description=confluent hypergeometric function,sort=Pagz} + +\begin{equation} +k_\nu(x) = \frac{2}{\pi}\int_0^{\pi/2}\cos(x \tan\theta - \nu\theta)\,d\theta +\end{equation} +\glossary{name=$k_\nu(x)$,description=Bateman's function,sort=kv} + +\chapter{Parabolic cylinder functions} + +\begin{equation} +D_p(z) = 2^{\frac{p}{2}}e^{-\frac{z^2}{4}} +\left\{ +\frac{\surd\pi}{\Gamma\left(\frac{1-p}{2}\right)} +\Phi\left(-\frac{p}{2},\frac{1}{2};\frac{z^2}{2}\right) +-\frac{\sqrt{2\pi}z}{\Gamma\left(-\frac{p}{2}\right)} +\Phi\left(\frac{1-p}{2},\frac{3}{2};\frac{z^2}{2}\right) +\right\} +\end{equation} +\glossary{name=$D_p(z)$,description=Parabolic cylinder functions,sort=Dp} + +\chapter{Elliptical Integral of the First Kind} + +\begin{equation} +F(\phi, k) = \int_0^\phi \frac{d\alpha}{\sqrt{1-k^2\sin^2\alpha}} +\end{equation} +\glossary{name={$F(\phi,k)$},description=Elliptical integral of the first kind,sort=Fpk} + +\chapter{Constants} + +\begin{equation} +C = 0.577\,215\,664\,901\ldots +\end{equation} +\glossary{name=$C$,description=Euler's constant,sort=C} + +\begin{equation} +G = 0.915\,965\,594\ldots +\end{equation} +\glossary{name=$G$,description=Catalan's constant,sort=G} + +\end{document} +\endinput +%% +%% End of file `sampleEq.tex'. |