summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/glossary/sampleEqPg.tex
blob: 06eca7839880e2a61ee908afc78acbdcb32ce9f7 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
%%
%% This is file `sampleEqPg.tex',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% glossary.dtx  (with options: `sampleEqPg.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,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
%%
%% End of file `sampleEqPg.tex'.