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267 lines
7.1 KiB
TeX
267 lines
7.1 KiB
TeX
%%
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%% This is file `sampleEq.tex',
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%% generated with the docstrip utility.
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%%
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%% The original source files were:
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%%
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%% glossary.dtx (with options: `sampleEq.tex,package')
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%% Copyright (C) 2006 Nicola Talbot, all rights reserved.
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%% If you modify this file, you must change its name first.
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%% You are NOT ALLOWED to distribute this file alone. You are NOT
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%% ALLOWED to take money for the distribution or use of either this
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%% file or a changed version, except for a nominal charge for copying
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%% etc.
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%% \CharacterTable
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%% {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
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%% 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
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%% Digits \0\1\2\3\4\5\6\7\8\9
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%% Exclamation \! Double quote \" Hash (number) \#
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%% Dollar \$ Percent \% Ampersand \&
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%% Acute accent \' Left paren \( Right paren \)
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%% Asterisk \* Plus \+ Comma \,
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%% Minus \- Point \. Solidus \/
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%% Colon \: Semicolon \; Less than \<
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%% Equals \= Greater than \> Question mark \?
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%% Commercial at \@ Left bracket \[ Backslash \\
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%% Right bracket \] Circumflex \^ Underscore \_
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%% Grave accent \` Left brace \{ Vertical bar \|
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%% Right brace \} Tilde \~}
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\documentclass[a4paper,12pt]{report}
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\usepackage{amsmath}
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\usepackage[colorlinks]{hyperref}
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\usepackage[header,border=none,cols=3,number=equation]{glossary}[2006/07/20]
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\newcommand{\erf}{\operatorname{erf}}
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\newcommand{\erfc}{\operatorname{erfc}}
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\makeglossary
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\renewcommand{\glossaryname}{Index of Special Functions
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and Notations}
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\renewcommand{\entryname}{Notation}
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\renewcommand{\descriptionname}{Function Name}
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\renewcommand{\glspageheader}{Number of Formula}
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\newcommand{\glossarysubheader}{ & & \\}
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\storeglosentry{Gamma}{name=\ensuremath{\Gamma(z)},
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description=Gamma function,sort=Gamma}
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\storeglosentry{gamma}{name={\ensuremath{\gamma(\alpha,x)}},
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description=Incomplete gamma function,sort=gamma}
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\storeglosentry{iGamma}{name={\ensuremath{\Gamma(\alpha,x)}},
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description=Incomplete gamma function,sort=Gamma}
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\storeglosentry{psi}{name=\ensuremath{\psi(x)},
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description=Psi function,sort=psi}
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\storeglosentry{erf}{name=\ensuremath{\erf(x)},
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description=Error function,sort=erf}
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\storeglosentry{erfc}{name=\ensuremath{\erfc},
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description=Complementary error function,sort=erfc}
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\storeglosentry{B}{name={\ensuremath{B(x,y)}},
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description=Beta function,sort=B}
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\storeglosentry{Bx}{name={\ensuremath{B_x(p,q)}},
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description=Incomplete beta function,sort=Bx}
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\storeglosentry{Tn}{name=\ensuremath{T_n(x)},
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description=Chebyshev's polynomials of the first kind,sort=Tn}
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\storeglosentry{Un}{name=\ensuremath{U_n(x)},
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description=Chebyshev's polynomials of the second kind,sort=Un}
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\storeglosentry{Hn}{name=\ensuremath{H_n(x)},
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description=Hermite polynomials,sort=Hn}
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\storeglosentry{Ln}{name=\ensuremath{L_n^\alpha(x)},
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description=Laguerre polynomials,sort=Lna}
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\storeglosentry{Znu}{name=\ensuremath{Z_\nu(z)},
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description=Bessel functions,sort=Z}
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\storeglosentry{Phi}{name={\ensuremath{\Phi(\alpha,\gamma;z)}},
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description=confluent hypergeometric function,sort=Pagz}
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\storeglosentry{knu}{name=\ensuremath{k_\nu(x)},
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description=Bateman's function,sort=kv}
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\storeglosentry{Dp}{name=\ensuremath{D_p(z)},
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description=Parabolic cylinder functions,sort=Dp}
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\storeglosentry{F}{name={\ensuremath{F(\phi,k)}},
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description=Elliptical integral of the first kind,sort=Fpk}
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\storeglosentry{C}{name=\ensuremath{C},
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description=Euler's constant,sort=C}
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\storeglosentry{G}{name=\ensuremath{G},
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description=Catalan's constant,sort=G}
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\begin{document}
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\title{A Sample Document Using glossary.sty}
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\author{Nicola Talbot}
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\maketitle
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\begin{abstract}
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This is a sample document illustrating the use of the \textsf{glossary}
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package. The functions here have been taken from ``Tables of
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Integrals, Series, and Products'' by I.S.~Gradshteyn and I.M~Ryzhik.
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The glossary is a list of special functions, so
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the equation number has been used rather than the page number. This
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can be done using the \texttt{number=equation} package
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option.
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\end{abstract}
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\printglossary
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\chapter{Gamma Functions}
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\begin{equation}
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\gls{Gamma} = \int_{0}^{\infty}e^{-t}t^{z-1}\,dt
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\end{equation}
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\verb|\ensuremath| is only required here if using
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hyperlinks.
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\begin{equation}
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\useGlosentry{Gamma}{\ensuremath{\Gamma(x+1)}} = x\Gamma(x)
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\end{equation}
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\begin{equation}
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\gls{gamma} = \int_0^x e^{-t}t^{\alpha-1}\,dt
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\end{equation}
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\begin{equation}
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\gls{iGamma} = \int_x^\infty e^{-t}t^{\alpha-1}\,dt
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\end{equation}
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\newpage
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\begin{equation}
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\gls{Gamma} = \Gamma(\alpha, x) + \gamma(\alpha, x)
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\end{equation}
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\begin{equation}
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\gls{psi} = \frac{d}{dx}\ln\Gamma(x)
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\end{equation}
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\chapter{Error Functions}
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\begin{equation}
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\gls{erf} = \frac{2}{\surd\pi}\int_0^x e^{-t^2}\,dt
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\end{equation}
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\begin{equation}
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\gls{erfc} = 1 - \erf(x)
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\end{equation}
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\chapter{Beta Function}
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\begin{equation}
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\gls{B} = 2\int_0^1 t^{x-1}(1-t^2)^{y-1}\,dt
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\end{equation}
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Alternatively:
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\begin{equation}
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\gls{B} = 2\int_0^{\frac\pi2}\sin^{2x-1}\phi\cos^{2y-1}\phi\,d\phi
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\end{equation}
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\begin{equation}
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\gls{B} = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)} = B(y,x)
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\end{equation}
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\begin{equation}
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\gls{Bx} = \int_0^x t^{p-1}(1-t)^{q-1}\,dt
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\end{equation}
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\chapter{Polynomials}
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\section{Chebyshev's polynomials}
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\begin{equation}
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\gls{Tn} = \cos(n\arccos x)
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\end{equation}
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\begin{equation}
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\gls{Un} = \frac{\sin[(n+1)\arccos x]}{\sin[\arccos x]}
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\end{equation}
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\section{Hermite polynomials}
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\begin{equation}
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\gls{Hn} = (-1)^n e^{x^2} \frac{d^n}{dx^n}(e^{-x^2})
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\end{equation}
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\section{Laguerre polynomials}
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\begin{equation}
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L_n^{\alpha} (x) = \frac{1}{n!}e^x x^{-\alpha}
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\frac{d^n}{dx^n}(e^{-x}x^{n+\alpha})
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\end{equation}
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\chapter{Bessel Functions}
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Bessel functions $Z_\nu$ are solutions of
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\begin{equation}
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\useglosentry{Znu}
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\frac{d^2Z_\nu}{dz^2} + \frac{1}{z}\,\frac{dZ_\nu}{dz} +
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\left( 1-\frac{\nu^2}{z^2}Z_\nu = 0 \right)
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\end{equation}
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\chapter{Confluent hypergeometric function}
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\begin{equation}
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\gls{Phi} = 1 + \frac{\alpha}{\gamma}\,\frac{z}{1!}
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+ \frac{\alpha(\alpha+1)}{\gamma(\gamma+1)}\,\frac{z^2}{2!}
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+\frac{\alpha(\alpha+1)(\alpha+2)}{\gamma(\gamma+1)(\gamma+2)}\,
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\frac{z^3}{3!} + \cdots
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\end{equation}
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\begin{equation}
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\gls{knu} = \frac{2}{\pi}\int_0^{\pi/2}
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\cos(x \tan\theta - \nu\theta)\,d\theta
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\end{equation}
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\chapter{Parabolic cylinder functions}
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\begin{equation}
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\gls{Dp} = 2^{\frac{p}{2}}e^{-\frac{z^2}{4}}
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\left\{
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\frac{\surd\pi}{\Gamma\left(\frac{1-p}{2}\right)}
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\Phi\left(-\frac{p}{2},\frac{1}{2};\frac{z^2}{2}\right)
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-\frac{\sqrt{2\pi}z}{\Gamma\left(-\frac{p}{2}\right)}
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\Phi\left(\frac{1-p}{2},\frac{3}{2};\frac{z^2}{2}\right)
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\right\}
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\end{equation}
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\chapter{Elliptical Integral of the First Kind}
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\begin{equation}
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\gls{F} = \int_0^\phi \frac{d\alpha}{\sqrt{1-k^2\sin^2\alpha}}
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\end{equation}
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\chapter{Constants}
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\begin{equation}
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\gls{C} = 0.577\,215\,664\,901\ldots
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\end{equation}
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\begin{equation}
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\gls{G} = 0.915\,965\,594\ldots
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\end{equation}
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\end{document}
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\endinput
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%%
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%% End of file `sampleEq.tex'.
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