path: root/Master/texmf-dist/doc/latex/glossary/sampleEqPg.tex

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%% glossary.dtx  (with options: `sampleEqPg.tex,package')
%% Copyright (C) 2005 Nicola Talbot, all rights reserved.
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\documentclass[a4paper,12pt]{report}

\usepackage{amsmath}
\usepackage[header,toc,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{\glossarypreamble}{Numbers in italic indicate the equation number,
numbers in bold indicate page numbers where the main definition occurs.\par}

\setglossary{glsnumformat=textit}

\renewcommand{\glossaryheader}{\bfseries Notation &
\multicolumn{2}{c}{\bfseries
\begin{tabular}{c}Name of the Function and\\the number of
the formula\end{tabular}}\\}

\renewcommand{\shortglossaryname}{Special Functions}

\makeglossary

\pagestyle{headings}

\begin{document}

\title{Sample Document Using Interchangable Numbering}
\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 lists both page number and equation numbers.  Since the
equation numbers depend on chapter numbers, the page compositor needs
to be redefined.  (Note that this example will only work where the
page number and equation number compositor is the same. So it won't work
if, say, the page numbers are of the form 2-4 and the equation numbers
are of the form 4.6)  As most of the glossary entries should have an italic
format, it is easiest to set the default format to italic.

\end{abstract}

\tableofcontents

\printglossary

\newcommand{\myglossary}[2]{%
\renewcommand{\theglossarynum}{#1}\glossary{#2}}

\newcommand{\glossarypage}[1]{%
\renewcommand{\theglossarynum}{\thepage}\glossary{#1,format=textbf}}
\newcommand{\glossaryequation}[1]{%
\renewcommand{\theglossarynum}{\theequation}\glossary{#1}}

\chapter{Gamma Functions}

The gamma function is defined as
\renewcommand{\theglossarynum}{\thepage}
\glossary{name=$\Gamma(z)$,description=Gamma function,sort=Gamma,format=textbf}
\renewcommand{\theglossarynum}{\theequation}
\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}

The error function is defined as:
\renewcommand{\theglossarynum}{\thepage}
\glossary{name=$\erf(x)$,description=Error function,sort=erf,format=textbf}
\renewcommand{\theglossarynum}{\theequation}
\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{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}

\chapter{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}

\chapter{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
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