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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) 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'.