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%%
%% This is file `sampleEq.tex',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% glossary.dtx (with options: `sampleEq.tex,package')
%% Copyright (C) 2006 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[colorlinks]{hyperref}
\usepackage[header,border=none,cols=3,number=equation]{glossary}[2006/07/20]
\newcommand{\erf}{\operatorname{erf}}
\newcommand{\erfc}{\operatorname{erfc}}
\makeglossary
\renewcommand{\glossaryname}{Index of Special Functions
and Notations}
\renewcommand{\entryname}{Notation}
\renewcommand{\descriptionname}{Function Name}
\renewcommand{\glspageheader}{Number of Formula}
\newcommand{\glossarysubheader}{ & & \\}
\storeglosentry{Gamma}{name=\ensuremath{\Gamma(z)},
description=Gamma function,sort=Gamma}
\storeglosentry{gamma}{name={\ensuremath{\gamma(\alpha,x)}},
description=Incomplete gamma function,sort=gamma}
\storeglosentry{iGamma}{name={\ensuremath{\Gamma(\alpha,x)}},
description=Incomplete gamma function,sort=Gamma}
\storeglosentry{psi}{name=\ensuremath{\psi(x)},
description=Psi function,sort=psi}
\storeglosentry{erf}{name=\ensuremath{\erf(x)},
description=Error function,sort=erf}
\storeglosentry{erfc}{name=\ensuremath{\erfc},
description=Complementary error function,sort=erfc}
\storeglosentry{B}{name={\ensuremath{B(x,y)}},
description=Beta function,sort=B}
\storeglosentry{Bx}{name={\ensuremath{B_x(p,q)}},
description=Incomplete beta function,sort=Bx}
\storeglosentry{Tn}{name=\ensuremath{T_n(x)},
description=Chebyshev's polynomials of the first kind,sort=Tn}
\storeglosentry{Un}{name=\ensuremath{U_n(x)},
description=Chebyshev's polynomials of the second kind,sort=Un}
\storeglosentry{Hn}{name=\ensuremath{H_n(x)},
description=Hermite polynomials,sort=Hn}
\storeglosentry{Ln}{name=\ensuremath{L_n^\alpha(x)},
description=Laguerre polynomials,sort=Lna}
\storeglosentry{Znu}{name=\ensuremath{Z_\nu(z)},
description=Bessel functions,sort=Z}
\storeglosentry{Phi}{name={\ensuremath{\Phi(\alpha,\gamma;z)}},
description=confluent hypergeometric function,sort=Pagz}
\storeglosentry{knu}{name=\ensuremath{k_\nu(x)},
description=Bateman's function,sort=kv}
\storeglosentry{Dp}{name=\ensuremath{D_p(z)},
description=Parabolic cylinder functions,sort=Dp}
\storeglosentry{F}{name={\ensuremath{F(\phi,k)}},
description=Elliptical integral of the first kind,sort=Fpk}
\storeglosentry{C}{name=\ensuremath{C},
description=Euler's constant,sort=C}
\storeglosentry{G}{name=\ensuremath{G},
description=Catalan's constant,sort=G}
\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 using the \texttt{number=equation} package
option.
\end{abstract}
\printglossary
\chapter{Gamma Functions}
\begin{equation}
\gls{Gamma} = \int_{0}^{\infty}e^{-t}t^{z-1}\,dt
\end{equation}
\verb|\ensuremath| is only required here if using
hyperlinks.
\begin{equation}
\useGlosentry{Gamma}{\ensuremath{\Gamma(x+1)}} = x\Gamma(x)
\end{equation}
\begin{equation}
\gls{gamma} = \int_0^x e^{-t}t^{\alpha-1}\,dt
\end{equation}
\begin{equation}
\gls{iGamma} = \int_x^\infty e^{-t}t^{\alpha-1}\,dt
\end{equation}
\newpage
\begin{equation}
\gls{Gamma} = \Gamma(\alpha, x) + \gamma(\alpha, x)
\end{equation}
\begin{equation}
\gls{psi} = \frac{d}{dx}\ln\Gamma(x)
\end{equation}
\chapter{Error Functions}
\begin{equation}
\gls{erf} = \frac{2}{\surd\pi}\int_0^x e^{-t^2}\,dt
\end{equation}
\begin{equation}
\gls{erfc} = 1 - \erf(x)
\end{equation}
\chapter{Beta Function}
\begin{equation}
\gls{B} = 2\int_0^1 t^{x-1}(1-t^2)^{y-1}\,dt
\end{equation}
Alternatively:
\begin{equation}
\gls{B} = 2\int_0^{\frac\pi2}\sin^{2x-1}\phi\cos^{2y-1}\phi\,d\phi
\end{equation}
\begin{equation}
\gls{B} = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} = B(y,x)
\end{equation}
\begin{equation}
\gls{Bx} = \int_0^x t^{p-1}(1-t)^{q-1}\,dt
\end{equation}
\chapter{Polynomials}
\section{Chebyshev's polynomials}
\begin{equation}
\gls{Tn} = \cos(n\arccos x)
\end{equation}
\begin{equation}
\gls{Un} = \frac{\sin[(n+1)\arccos x]}{\sin[\arccos x]}
\end{equation}
\section{Hermite polynomials}
\begin{equation}
\gls{Hn} = (-1)^n e^{x^2} \frac{d^n}{dx^n}(e^{-x^2})
\end{equation}
\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}
\chapter{Bessel Functions}
Bessel functions $Z_\nu$ are solutions of
\begin{equation}
\useglosentry{Znu}
\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}
\chapter{Confluent hypergeometric function}
\begin{equation}
\gls{Phi} = 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}
\begin{equation}
\gls{knu} = \frac{2}{\pi}\int_0^{\pi/2}
\cos(x \tan\theta - \nu\theta)\,d\theta
\end{equation}
\chapter{Parabolic cylinder functions}
\begin{equation}
\gls{Dp} = 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}
\chapter{Elliptical Integral of the First Kind}
\begin{equation}
\gls{F} = \int_0^\phi \frac{d\alpha}{\sqrt{1-k^2\sin^2\alpha}}
\end{equation}
\chapter{Constants}
\begin{equation}
\gls{C} = 0.577\,215\,664\,901\ldots
\end{equation}
\begin{equation}
\gls{G} = 0.915\,965\,594\ldots
\end{equation}
\end{document}
\endinput
%%
%% End of file `sampleEq.tex'.
|
