diff options
author | Karl Berry <karl@freefriends.org> | 2006-09-25 23:46:58 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2006-09-25 23:46:58 +0000 |
commit | d4f96dc70d6aad918f541123e66589a2e44e18f1 (patch) | |
tree | bc933bc54a70e3ab4cf699a6c2d778b062287d16 /Master/texmf-dist/doc/latex/cool | |
parent | 66d540bf33713d5f36291b9e7c8a8f8039aebdb4 (diff) |
new package cool (25sep06)
git-svn-id: svn://tug.org/texlive/trunk@2199 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/cool')
-rw-r--r-- | Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.pdf | bin | 0 -> 159960 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.tex | 2225 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/cool/README | 43 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/cool/cool.pdf | bin | 0 -> 311475 bytes |
4 files changed, 2268 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.pdf b/Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.pdf Binary files differnew file mode 100644 index 00000000000..0bff259ca5b --- /dev/null +++ b/Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.pdf diff --git a/Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.tex b/Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.tex new file mode 100644 index 00000000000..4a2d5f757b1 --- /dev/null +++ b/Master/texmf-dist/doc/latex/cool/Content_LaTeX_Package_Demo.tex @@ -0,0 +1,2225 @@ +\documentclass[12pt]{article} % Specifies the document class + +% The preamble begins here. + +%<-------------------------------------------Included Packages----------------------------------------------------> +%\usepackage[dvips]{epsfig} + % for displaying pictures +%\usepackage[b]{esvect} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{ifthen} +\usepackage{cool} +\usepackage{makeidx} +\makeindex +%<-----------------------------------------End Included Packages--------------------------------------------------> + + +%<------------------------------------------Document Properties---------------------------------------------------> +\title{Content \LaTeXe} % Declares the document's title. +\author{N. Setzer} % Declares the author's name. +%\date{} % Declares the date. Aren't you glad you have that kind of power? +%\setlength{\topmargin}{-0.8in} +%\setlength{\topskip}{0.2in} % between header and text +%\setlength{\textheight}{9.0in} % height of main text +%\setlength{\textwidth}{7.3in} % width of text +%\setlength{\oddsidemargin}{-0.4in} % odd page left margin +%\setlength{\evensidemargin}{-0.4in} % even page left margin +%<----------------------------------------End Document Properties-------------------------------------------------> + + +%<----------------------------------------Modified LaTeX Command Definitions---------------------------------------> +\newcommand{\var}[1]{} +\newenvironment{declaration}{\hide}{} +\newcommand{\hide}[1]{} +\newenvironment{derivation}{\begin{eqnarray*}}{\end{eqnarray*}} +\newenvironment{der}{\begin{eqnarray*}}{\end{eqnarray*}} +%<--------------------------------------End Modified LaTeX Command Definitions-------------------------------------> + +%<-------------------------------------------Command Definitions---------------------------------------------------> +%%%%%%%%%%%%% Formatting +\newcommand{\headerRow}{\bf \textrm Command & \bf \textrm Inline & \bf \textrm Display \\} +%%%%%%%%%%%%% Indexing +\newcommand{\bs}{\symbol{'134}}% backslash +\newcommand{\idxc}[2][]{\texttt{\bs#2}\index{#2#1@\texttt{\bs#2}#1}} +%<-----------------------------------------End Command Definitions-------------------------------------------------> + + +%############################################Sectioning Templates################################################### + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section{} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%\subsection{} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%\subsubsection{} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% +%\subsubsubsection{} +%%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% | % | % | % | % | % | % | % | % | % | % | % | % | % | % | +%\appendix +% | % | % | % | % | % | % | % | % | % | % | % | % | % | % | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +%##########################################End Sectioning Templates################################################# + + +\begin{document} % End of preamble and beginning of text. + +\maketitle + + +%%%%%%%%%%%%%% IMPORTANT: we can have seemingly UNLIMITE number of booleans !!!!!! +%%%%%%%%%%%%%% however, we can only create an 'array' of 746 of them + +% STRING capacity exceeded---this just won't work the way you want it to. +%\newcounter{testing} +%\setcounter{testing}{0} +%\whiledo{\value{testing}<6430}% +%{% +%\addtocounter{testing}{1}% +%\newboolean{j\arabic{testing}}% +%} + +% no errors but is not effective +%\newcounter{arrayTrav} +%\def\newarray#1#2{\def#1##1{% +%\ifthenelse{\equal{##1}{length}} +% {% +% #2 +% }% +%% Else +%\ifcase##1{0} +%\forLoop{1}{#2}{arrayTrav}% +% {% +% \or{0} +% }% +%\fi +%}} +%\def\setval#1#2#3{% +%\def#1##1{% +%\ifcase##1% +%\forLoop{1}{#1{length}}{arrayTrav} +% {% +% \or +% \ifthenelse{\value{arrayTrav}=#2} +% {#3} +% {#1{\arabic{arrayTrav}}} +% }% +%\fi +%}} +% +%\newarray{\joker}{10} +%\joker{2} +%\setval{\joker}{2}{t} +%\joker{2} + + +%% Works but costs alot of counters and only allows integers and single characters +%\newcommand{\newarray}[3][0]{% +%\newcounter{length#2}% +%\setcounter{length#2}{#3} +%\newcounter{fill#2} +%\forLoop{1}{\value{length#2}}{fill#2}% +% {% +% \newcounter{values#2\arabic{fill#2}} +% \setcounter{values#2\arabic{fill#2}}{#1} +% }% +%} +% +%\newcommand{\newstring}[3][0]{% +%\newcounter{strlen#2}% +%\setcounter{strlen#2}{#3} +%\newcounter{charfill#2} +%\forLoop{1}{\value{strlen#2}}{charfill#2}% +% {% +% \newcounter{strchar#2\arabic{charfill#2}} +% \setcounter{strchar#2\arabic{charfill#2}}{`#1} +% }% +%} +%\newcommand{\setchar}[3]{\setcounter{strchar#1#2}{`#3}} +%\newcommand{\strchar}[2]{\char\value{strchar#1#2}} +%\newcommand{\setstr}[2] +%{% +%\forLoop{1}{\value{strlen#1}}{charfill#1}% +% {% +% }% +%} +% +%\newcommand{\setval}[3]{\setcounter{values#1#2}{#3}} +%\newcommand{\arrayval}[2]{\arabic{values#1#2}} +% +%\newarray{joker}{13} +% +%\arrayval{joker}{2} +%\setval{joker}{2}{3} +%\arrayval{joker}{2} +%\setval{joker}{3}{12} +%\arrayval{joker}{3} +% +%\newstring{string}{114} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Commands} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +\label{Section:Commands} +% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Constants} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +\headerRow +\idxc[ ($\sqrt{-1}$)]{I} & $\I$ & $\displaystyle \I$ \\ +\idxc[ (base of natural log)]{E}& $\E$ & $\displaystyle \E$ \\ +\idxc{PI} & $\PI$ & $\displaystyle \PI$ \\ +\idxc{GoldenRatio} & $\GoldenRatio$ & $\displaystyle \GoldenRatio$ \\ +\idxc{EulerGamma} & $\EulerGamma$ & $\displaystyle \EulerGamma$ \\ +\idxc{Catalan} & $\Catalan$ & $\displaystyle \Catalan$ \\ +\idxc{Glaisher} & $\Glaisher$ & $\displaystyle \Glaisher$ \\ +\idxc{Khinchin} & $\Khinchin$ & $\displaystyle \Khinchin$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Symbols} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +\idxc{Infinity} & $\Infinity$ & $\displaystyle \Infinity$ \\ +\idxc{Indeterminant} & $\Indeterminant$ & $\displaystyle \Indeterminant$ \\ +\idxc{DirectedInfinity}\verb|{z}| & $\DirectedInfinity{z}$ & $\displaystyle \DirectedInfinity{z}$ \\ +\idxc{DirInfty}\verb|{z}| & $\DirInfty{z}$ & $\displaystyle \DirInfty{z}$ \\ +\idxc{ComplexInfinity} & $\ComplexInfinity$ & $\displaystyle \ComplexInfinity$ \\ +\idxc{CInfty} & $\CInfty$ & $\displaystyle \CInfty$ \\ +\end{tabular} +\end{center} + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Exponential and Logarithmic Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +\headerRow +\idxc{Exp}\verb|{5x}| & $\Exp{5x}$ & $\displaystyle \Exp{5x}$ \\ +\verb|\Style{ExpParen=b}|% +\Style{ExpParen=b} \\ +\idxc{Exp}\verb|{5x}| & $\Exp{5x}$ & $\displaystyle \Exp{5x}$ \\ +\verb|\Style{ExpParen=br}|% +\Style{ExpParen=br} \\ +\idxc{Exp}\verb|{5x}| & $\Exp{5x}$ & $\displaystyle \Exp{5x}$ \\ +\idxc{Log}\verb|{5}| & $\Log{5}$ & $\displaystyle \Log{5}$ \\ +\idxc{Log}\verb|[10]{5}| & $\Log[10]{5}$ & $\displaystyle \Log[10]{5}$ \\ +\idxc{Log}\verb|[4]{5}| & $\Log[4]{5}$ & $\displaystyle \Log[4]{5}$ \\ +\verb|\Style{LogBaseESymb=log}|% +\Style{LogBaseESymb=log} \\ +\idxc{Log}\verb|{5}| & $\Log{5}$ & $\displaystyle \Log{5}$ \\ +\idxc{Log}\verb|[10]{5}| & $\Log[10]{5}$ & $\displaystyle \Log[10]{5}$ \\ +\idxc{Log}\verb|[4]{5}| & $\Log[4]{5}$ & $\displaystyle \Log[4]{5}$ \\ +\verb|\Style{LogShowBase=always}|% +\Style{LogBaseESymb=ln}% +\Style{LogShowBase=always} \\ +\idxc{Log}\verb|{5}| & $\Log{5}$ & $\displaystyle \Log{5}$ \\ +\idxc{Log}\verb|[10]{5}| & $\Log[10]{5}$ & $\displaystyle \Log[10]{5}$ \\ +\idxc{Log}\verb|[4]{5}| & $\Log[4]{5}$ & $\displaystyle \Log[4]{5}$ \\ +\verb|\Style{LogShowBase=at will}|% +\Style{LogShowBase=at will} \\ +\idxc{Log}\verb|{5}| & $\Log{5}$ & $\displaystyle \Log{5}$ \\ +\idxc{Log}\verb|[10]{5}| & $\Log[10]{5}$ & $\displaystyle \Log[10]{5}$ \\ +\idxc{Log}\verb|[4]{5}| & $\Log[4]{5}$ & $\displaystyle \Log[4]{5}$ \\ +\verb|\Style{LogParen=p}|% +\Style{LogParen=p} \\ +\idxc{Log}\verb|[4]{5}| & $\Log[4]{5}$ & $\displaystyle \Log[4]{5}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Trigonometric Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Trigonometric Functions} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Trigonometric Functions +\idxc{Sin}\verb|{x}| & $\Sin{x}$ & $\displaystyle \Sin{x}$ \\ +\idxc{Cos}\verb|{x}| & $\Cos{x}$ & $\displaystyle \Cos{x}$ \\ +\idxc{Tan}\verb|{x}| & $\Tan{x}$ & $\displaystyle \Tan{x}$ \\ +\idxc{Csc}\verb|{x}| & $\Csc{x}$ & $\displaystyle \Csc{x}$ \\ +\idxc{Sec}\verb|{x}| & $\Sec{x}$ & $\displaystyle \Sec{x}$ \\ +\idxc{Cot}\verb|{x}| & $\Cot{x}$ & $\displaystyle \Cot{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Inverse Trigonometric Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Trigonometric Functions!Inverse} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Inverse Trigonometric Functions +\Style{ArcTrig=inverse}% +\verb|\Style{ArcTrig=inverse}| (default)% + \\ +\idxc{ArcSin}\verb|{x}| & $\ArcSin{x}$ & $\displaystyle \ArcSin{x}$ \\ +\idxc{ArcCos}\verb|{x}| & $\ArcCos{x}$ & $\displaystyle \ArcCos{x}$ \\ +\idxc{ArcTan}\verb|{x}| & $\ArcTan{x}$ & $\displaystyle \ArcTan{x}$ \\ +% +\Style{ArcTrig=arc}% +\verb|\Style{ArcTrig=arc}|% + \\ +\idxc{ArcSin}\verb|{x}| & $\ArcSin{x}$ & $\displaystyle \ArcSin{x}$ \\ +\idxc{ArcCos}\verb|{x}| & $\ArcCos{x}$ & $\displaystyle \ArcCos{x}$ \\ +\idxc{ArcTan}\verb|{x}| & $\ArcTan{x}$ & $\displaystyle \ArcTan{x}$ \\ + \\ +\idxc{ArcCsc}\verb|{x}| & $\ArcCsc{x}$ & $\displaystyle \ArcCsc{x}$ \\ +\idxc{ArcSec}\verb|{x}| & $\ArcSec{x}$ & $\displaystyle \ArcSec{x}$ \\ +\idxc{ArcCot}\verb|{x}| & $\ArcCot{x}$ & $\displaystyle \ArcCot{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Hyberbolic Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Hyperbolic Functions} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Hyperbolic Functions +\idxc{Sinh}\verb|{x}| & $\Sinh{x}$ & $\displaystyle \Sinh{x}$ \\ +\idxc{Cosh}\verb|{x}| & $\Cosh{x}$ & $\displaystyle \Cosh{x}$ \\ +\idxc{Tanh}\verb|{x}| & $\Tanh{x}$ & $\displaystyle \Tanh{x}$ \\ +\idxc{Csch}\verb|{x}| & $\Csch{x}$ & $\displaystyle \Csch{x}$ \\ +\idxc{Sech}\verb|{x}| & $\Sech{x}$ & $\displaystyle \Sech{x}$ \\ +\idxc{Coth}\verb|{x}| & $\Coth{x}$ & $\displaystyle \Coth{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Inverse Hyberbolic Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Hyperbolic Functions!Inverse} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Inverse Hyberbolic Functions +\idxc{ArcSinh}\verb|{x}| & $\ArcSinh{x}$ & $\displaystyle \ArcSinh{x}$ \\ +\idxc{ArcCosh}\verb|{x}| & $\ArcCosh{x}$ & $\displaystyle \ArcCosh{x}$ \\ +\idxc{ArcTanh}\verb|{x}| & $\ArcTanh{x}$ & $\displaystyle \ArcTanh{x}$ \\ +\idxc{ArcCsch}\verb|{x}| & $\ArcCsch{x}$ & $\displaystyle \ArcCsch{x}$ \\ +\idxc{ArcSech}\verb|{x}| & $\ArcSech{x}$ & $\displaystyle \ArcSech{x}$ \\ +\idxc{ArcCoth}\verb|{x}| & $\ArcCoth{x}$ & $\displaystyle \ArcCoth{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Product Logarithms} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Lambert Function} +\index{Lambert Function!Generalized} +\index{Generalized Lambert Function} +\index{Product Logarithms} +\index{Logarithms!Product} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%%% Lambert Function +\idxc{LambertW}\verb|{z}| & $\LambertW{z}$ & $\displaystyle \LambertW{z}$ \\ +%%%%%%%% Lambert Function +\idxc{ProductLog}\verb|{z}| & $\ProductLog{z}$ & $\displaystyle \ProductLog{z}$ \\ + \\ + +%%%%%%% Generalized Lambert Function +\idxc{LambertW}\verb|{k,z}| & $\LambertW{k,z}$ & $\displaystyle \LambertW{k,z}$ \\ +%%%%%%%% Generalized Lambert Function +\idxc{ProductLog}\verb|{k,z}| & $\ProductLog{k,z}$ & $\displaystyle \ProductLog{k,z}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Max and Min} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Max and Min +\idxc{Max}\verb|{1,2,3,4,5}| & $\Max{1,2,3,4,5}$ & $\displaystyle \Max{1,2,3,4,5}$ \\ +\idxc{Min}\verb|{1,2,3,4,5}| & $\Min{1,2,3,4,5}$ & $\displaystyle \Min{1,2,3,4,5}$ +\end{tabular} +\end{center} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Bessel, Airy, and Struve Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Bessel} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Bessel functions can be `renamed' with the \verb|\Style| tag. For example, \verb|\Style{BesselYSymb=N}| yields \Style{BesselYSymb=N} $\BesselY{\nu}{x}$ \Style{BesselYSymb=Y} + +\index{Bessel Functions} + + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Bessel +% Bessel Function of the first Kind +\idxc{BesselJ}\verb|{0}{x}| & $\BesselJ{0}{x}$ & $\displaystyle \BesselJ{0}{x}$ \\ +% Bessel Function of the second Kind +\idxc{BesselY}\verb|{0}{x}| & $\BesselY{0}{x}$ & $\displaystyle \BesselY{0}{x}$ \\ +% Modified Bessel Function of the first Kind +\idxc{BesselI}\verb|{0}{x}| & $\BesselI{0}{x}$ & $\displaystyle \BesselI{0}{x}$ \\ +% Modified Bessel Function of the second Kind +\idxc{BesselK}\verb|{0}{x}| & $\BesselK{0}{x}$ & $\displaystyle \BesselK{0}{x}$ \\ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Airy} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Airy Functions} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Airy +\idxc{AiryAi}\verb|{x}| & $\AiryAi{x}$ & $\displaystyle \AiryAi{x}$ \\ +\idxc{AiryBi}\verb|{x}| & $\AiryBi{x}$ & $\displaystyle \AiryBi{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Struve} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Struve Functions} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Struve +\idxc{StruveH}\verb|{\nu}{x}| & $\StruveH{\nu}{x}$ & $\displaystyle \StruveH{\nu}{x}$ \\ +\idxc{StruveL}\verb|{\nu}{x}| & $\StruveL{\nu}{x}$ & $\displaystyle \StruveL{\nu}{x}$ +\end{tabular} +\end{center} + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Integer Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +\headerRow +% Floor +\idxc{Floor}\verb|{x}| & $\Floor{x}$ & $\displaystyle \Floor{x}$ \\ +\idxc{Ceiling}\verb|{x}| & $\Ceiling{x}$ & $\displaystyle \Ceiling{x}$ \\ +\idxc{Round}\verb|{x}| & $\Round{x}$ & $\displaystyle \Round{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{int@\textrm{int}|see{\texttt{\bs iPart}}} +\index{frac@\textrm{frac}|see{\texttt{\bs fPart}}} + +\begin{center} +\begin{tabular}{ccc} +\idxc{iPart}\verb|{x}| & $\iPart{x}$ & $\displaystyle \iPart{x}$ \\ +\idxc{IntegerPart}\verb|{x}| & $\IntegerPart{x}$ & $\displaystyle \IntegerPart{x}$ \\ +\idxc{fPart}\verb|{x}| & $\fPart{x}$ & $\displaystyle \fPart{x}$ \\ +\idxc{FractionalPart}\verb|{x}| & $\FractionalPart{x}$ & $\displaystyle \FractionalPart{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Greatest Common Divisor} +\index{Least Common Multiple} + +\begin{center} +\begin{tabular}{ccc} +\verb|\Style{ModDisplay=mod}| (default)% +\Style{ModDisplay=mod} \\ +\idxc{Mod}\verb|{m}{n}| & $\Mod{m}{n}$ & $\displaystyle \Mod{m}{n}$ \\ +\verb|\Style{ModDisplay=bmod}|% +\Style{ModDisplay=bmod} \\ +\idxc{Mod}\verb|{m}{n}| & $\Mod{m}{n}$ & $\displaystyle \Mod{m}{n}$ \\ +\verb|\Style{ModDisplay=pmod}|% +\Style{ModDisplay=pmod} \\ +\idxc{Mod}\verb|{m}{n}| & $\Mod{m}{n}$ & $\displaystyle \Mod{m}{n}$ \\ +\verb|\Style{ModDisplay=pod}|% +\Style{ModDisplay=pod} \\ +\idxc{Mod}\verb|{m}{n}| & $\Mod{m}{n}$ & $\displaystyle \Mod{m}{n}$ \\ + \\ +\idxc{Quotient}\verb|{m}{n}| & $\Quotient{m}{n}$ & $\displaystyle \Quotient{m}{n}$ \\ +\idxc{GCD}\verb|{m, n}| & $\GCD{m, n}$ & $\displaystyle \GCD{m, n}$ \\ +\idxc{ExtendedGCD}\verb|{m}{n}| & $\ExtendedGCD{m}{n}$ & $\displaystyle \ExtendedGCD{m}{n}$ \\ +\idxc{EGCD}\verb|{m}{n}| & $\EGCD{m}{n}$ & $\displaystyle \EGCD{m}{n}$ \\ +\idxc{LCM}\verb|{m, n}| & $\LCM{m, n}$ & $\displaystyle \LCM{m, n}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Fibonacci Number} + +\begin{center} +\begin{tabular}{ccc} +\idxc{Fibonacci}\verb|{\nu}| & $\Fibonacci{\nu}$ & $\displaystyle \Fibonacci{\nu}$ \\ +\idxc{Euler}\verb|{m}| & $\Euler{m}$ & $\displaystyle \Euler{m}$ \\ +\idxc{Bernoulli}\verb|{m}| & $\Bernoulli{m}$ & $\displaystyle \Bernoulli{m}$ \\ +\idxc{StirlingSOne}\verb|{n}{m}| & $\StirlingSOne{n}{m}$ & $\displaystyle \StirlingSOne{n}{m}$ \\ +\idxc{StirlingSTwo}\verb|{n}{m}| & $\StirlingSTwo{n}{m}$ & $\displaystyle \StirlingSTwo{n}{m}$ \\ +\idxc{PartitionsP}\verb|{n}| & $\PartitionsP{n}$ & $\displaystyle \PartitionsP{n}$ \\ +\idxc{PartitionsQ}\verb|{n}| & $\PartitionsQ{n}$ & $\displaystyle \PartitionsQ{n}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\idxc{DiscreteDelta}\verb|{n, m}| & $\DiscreteDelta{n, m}$ & $\displaystyle \DiscreteDelta{n, m}$ + \\ +\idxc{KroneckerDelta}\verb|{n m}| & $\KroneckerDelta{n m}$ & $\displaystyle \KroneckerDelta{n m}$ + \\ +\idxc{KroneckerDelta}\verb|[d]{n m}| & $\KroneckerDelta[d]{n m}$ & $\displaystyle \KroneckerDelta[d]{n m}$ + \\ +\idxc{LeviCivita}\verb|{i j k}| & $\LeviCivita{i j k}$ & $\displaystyle \LeviCivita{i j k}$ + \\ +\idxc{LeviCivita}\verb|[d]{i j k}| & $\LeviCivita[d]{i j k}$ & $\displaystyle \LeviCivita[d]{i j k}$ + \\ +\idxc{Signature}\verb|{i j k}| & $\Signature{i j k}$ & $\displaystyle \Signature{i j k}$ + \\ +\verb|\Style{LeviCivitaIndicies=up}|% +\Style{LeviCivitaIndicies=up} \\ +\idxc{LeviCivita}\verb|[d]{i j k}| & $\LeviCivita[d]{i j k}$ & $\displaystyle \LeviCivita[d]{i j k}$ + \\ +\verb|\Style{LeviCivitaIndicies=local}|% +\Style{LeviCivitaIndicies=local} \\ +\idxc{LeviCivita}\verb|[d]{i j k}| & $\LeviCivita[d]{i j k}$ & $\displaystyle \LeviCivita[d]{i j k}$ + \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Polynomials} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Polynomials can be `renamed' with the \verb|\Style| command: + +\begin{center} +\verb|\Style{| $\langle\mbox{\textit{Polynomial command} }\rangle$% + \verb|Symb=|$\langle\mbox{\textit{Symbol} }\rangle$% + \verb|}| +\end{center} + +As in \verb|\Style{HermiteHSymb=h,LegendrePSymb=p}| \verb|$\HermiteH{n}{x}$| \verb|$\LegendreP{n,x}$| yielding: +\Style{HermiteHSymb=h,LegendrePSymb=p} $\HermiteH{n}{x}$ $\LegendreP{n,x}$ +\Style{HermiteHSymb=H,LegendrePSymb=P} + +\index{Polynomials!Hermite} +\index{Polynomials!Laugerre} +\index{Polynomials!Legendre} +\index{Polynomials!Chebyshev} +\index{Polynomials!Jacobi} +\index{Polynomials!Gegenbauer} +\index{Polynomials!Cyclotomic} +\index{Polynomials!Fibonacci} +\index{Polynomials!Euler} +\index{Polynomials!Bernoulli} +\index{Generalized Laugerre} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +% Hermite H +\idxc{HermiteH}\verb|{n}{x}| & $\HermiteH{n}{x}$ & $\displaystyle \HermiteH{n}{x}$ \\ +% Laugerre L +\idxc{LaugerreL}\verb|{n,x}| & $\LaugerreL{n,x}$ & $\displaystyle \LaugerreL{n,x}$ \\ +% Legendre P +\idxc{LegendreP}\verb|{n,x}| & $\LegendreP{n,x}$ & $\displaystyle \LegendreP{n,x}$ \\ +% Chebyshev T +\idxc{ChebyshevT}\verb|{n}{x}| & $\ChebyshevT{n}{x}$ & $\displaystyle \ChebyshevT{n}{x}$ \\ +% Chebyshev U +\idxc{ChebyshevU}\verb|{n}{x}| & $\ChebyshevU{n}{x}$ & $\displaystyle \ChebyshevU{n}{x}$ \\ +% Jacobi P +\idxc{JacobiP}\verb|{n}{a}{b}{x}| & $\JacobiP{n}{a}{b}{x}$& $\displaystyle \JacobiP{n}{a}{b}{x}$ \\ + \\ +% Associated Legendre P +\idxc{AssocLegendreP}\verb|{\ell}{m}{x}| + & $\AssocLegendreP{\ell}{m}{x}$ + & $\displaystyle \AssocLegendreP{\ell}{m}{x}$ + \\ +% Associated Legendre Q +\idxc{AssocLegendreQ}\verb|{\ell}{m}{x}| + & $\AssocLegendreQ{\ell}{m}{x}$ + & $\displaystyle \AssocLegendreQ{\ell}{m}{x}$ + \\ +% Generalized Laugerre Polynomial +\idxc{LaugerreL}\verb|{n,\lambda,x}| + & $\LaugerreL{n,\lambda,x}$ + & $\displaystyle \LaugerreL{n,\lambda,x}$ + \\ +% Gegenbauer Polynomial +\idxc{GegenbauerC}\verb|{n}{\lambda}{x}| + & $\GegenbauerC{n}{\lambda}{x}$ + & $\displaystyle \GegenbauerC{n}{\lambda}{x}$ + \\ +% Spherical Harmonics +\idxc{SphericalHarmY}\verb|{n}{m}{\theta}{\phi}| + & $\SphericalHarmY{n}{m}{\theta}{\phi}$ + & $\displaystyle \SphericalHarmY{n}{m}{\theta}{\phi}$ + \\ + \\ +% Cyclotomic +\idxc{CyclotomicC}\verb|{n}{x}| & $\CyclotomicC{n}{x}$ & $\displaystyle \CyclotomicC{n}{x}$ \\ +% Fibonacci +\idxc{FibonacciF}\verb|{n}{x}| & $\FibonacciF{n}{x}$ & $\displaystyle \FibonacciF{n}{x}$ \\ +% Euler +\idxc{EulerE}\verb|{n}{x}| & $\EulerE{n}{x}$ & $\displaystyle \EulerE{n}{x}$ \\ +% Bernoulli +\idxc{BernoulliB}\verb|{n}{x}| & $\BernoulliB{n}{x}$ & $\displaystyle \BernoulliB{n}{x}$ \\ +\end{tabular} +\end{center} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Gamma, Beta, and Error Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Factorials} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%% Gamma, Beta, Error Functions +\begin{center} + +\begin{tabular}{ccc} +\headerRow +%%%%%% Factorial +\idxc{Factorial}\verb|{n}| & $\Factorial{n}$ & $\displaystyle \Factorial{n}$ \\ +\idxc{DblFactorial}\verb|{n}| & $\DblFactorial{n}$ & $\displaystyle \DblFactorial{n}$ \\ +\idxc{Binomial}\verb|{n}{k}| & $\Binomial{n}{k}$ & $\displaystyle \Binomial{n}{k}$ \\ +\idxc{Multinomial}\verb|{1,2,3,4}| & $\Multinomial{1,2,3,4}$ + & $\displaystyle \Multinomial{1,2,3,4}$ \\ +\end{tabular} + +\vspace{0.25cm} + +\begin{tabular}{c} +\idxc{Multinomial}\verb|{n_1, n_2, \ldots, n_m}| +\\ + \begin{tabular}{cc} + {\bf Inline:} & $\Multinomial{n_1,n_2,\ldots,n_m}$ \\ + {\bf Display:} & $\displaystyle \Multinomial{n_1, n_2, \ldots, n_m}$ \\ + \end{tabular} +\\ +\\ +\end{tabular} + +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Gamma Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Incomplete Gamma Function} +\index{Gamma Functions} +\index{Gamma Functions!Inverse} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Gamma Functions +\idxc{GammaFunc}\verb|{x}| & $\GammaFunc{x}$ & $\displaystyle \GammaFunc{x}$ \\ +% incomplete Gamma function G(a,x) +\idxc{IncGamma}\verb|{a}{x}| & $\IncGamma{a}{x}$ & $\displaystyle \IncGamma{a}{x}$ \\ +% Generalized Incomplete Gamma G(a, x, y) +\idxc{GenIncGamma}\verb|{a}{x}{y}| & $\GenIncGamma{a}{x}{y}$ + & $\displaystyle \GenIncGamma{a}{x}{y}$ \\ +% Regularized Incomplete Gamma Q(a,x) +\idxc{RegIncGamma}\verb|{a}{x}| & $\RegIncGamma{a}{x}$ & $\displaystyle \RegIncGamma{a}{x}$ \\ +% Inverse of Regularized Incomplete Gamma InvQ(a,x) +% \ArcRegIncGamma +\idxc{RegIncGammaInv}\verb|{a}{x}| & $\RegIncGammaInv{a}{x}$ + & $\displaystyle \RegIncGammaInv{a}{x}$ \\ +% Generalized Regularized Incomplete Gamma Q(a, x, y) +\idxc{GenRegIncGamma}\verb|{a}{x}{y}| + & $\GenRegIncGamma{a}{x}{y}$ + & $\displaystyle \GenRegIncGamma{a}{x}{y}$ + \\ +% Inverse of Gen. Reg. Incomplete Gamma InvQ(a, x, y) +% \ArcGenRegIncGamma +\idxc{GenRegIncGammaInv}\verb|{a}{x}{y}| + & $\GenRegIncGammaInv{a}{x}{y}$ + & $\displaystyle \GenRegIncGammaInv{a}{x}{y}$ + \\ +% Pochhammer Symbol (a)_n +\idxc{Pochhammer}\verb|{a}{n}| & $\Pochhammer{a}{n}$ & $\displaystyle \Pochhammer{a}{n}$ \\ +% Log Gamma Func +\idxc{LogGamma}\verb|{x}| & $\LogGamma{x}$ & $\displaystyle \LogGamma{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Derivatives of Gamma Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Derivatives!of Gamma Functions} +\index{Beta Functions} +\index{Beta Functions!Inverse} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Derivative of Gamma Functions +% Digamma function +\idxc{DiGamma}\verb|{x}| & $\DiGamma{x}$ & $\displaystyle \DiGamma{x}$ \\ +% PolyGamma function psi^(\nu) (x) +\idxc{PolyGamma}\verb|{\nu}{x}| & $\PolyGamma{\nu}{x}$ & $\displaystyle \PolyGamma{\nu}{x}$ \\ +% Harmonic Number H_x +\idxc{HarmNum}\verb|{x}| & $\HarmNum{x}$ & $\displaystyle \HarmNum{x}$ \\ +% Generalized Harmonic Number H_x^(r) +\idxc{HarmNum}\verb|{x,r}| & $\HarmNum{x,r}$ & $\displaystyle \HarmNum{x,r}$ \\ +% Beta Function B(a, b) +\idxc{Beta}\verb|{a,b}| & $\Beta{a,b}$ & $\displaystyle \Beta{a,b}$ \\ +% Incomplete Beta Function B_z(a, b) +\idxc{IncBeta}\verb|{z}{a}{b}| & $\IncBeta{z}{a}{b}$ & $\displaystyle \IncBeta{z}{a}{b}$ \\ +% Generalized Inc. Beta Func. B_(x,y) (a, b) +\idxc{GenIncBeta}\verb|{x}{y}{a}{b}| + & $\GenIncBeta{x}{y}{a}{b}$ + & $\displaystyle \GenIncBeta{x}{y}{a}{b}$ + \\ +% Regularized Incomplete Beta Function I_z(a,b) +\idxc{RegIncBeta}\verb|{z}{a}{b}| & $\RegIncBeta{z}{a}{b}$ + & $\displaystyle \RegIncBeta{z}{a}{b}$ \\ +% Inverse of Reg. Incomplete Beta Function InvI_z(a,b) +% \ArcRegIncBeta +\idxc{RegIncBetaInv}\verb|{z}{a}{b}| + & $\RegIncBetaInv{z}{a}{b}$ + & $\displaystyle \RegIncBetaInv{z}{a}{b}$ + \\ +% Gen. Regularized Inc. Beta Func. I_(x,y) (a, b) +\idxc{GenRegIncBeta}\verb|{x}{y}{a}{b}| + & $\GenRegIncBeta{x}{y}{a}{b}$ + & $\displaystyle \GenRegIncBeta{x}{y}{a}{b}$ + \\ +% Inv. of Gen. Reg. Inc. Beta InvI_(x,y) (a, b) +%\ArcGenRegIncBeta +\idxc{GenRegIncBetaInv}\verb|{x}{y}{a}{b}| + & $\GenRegIncBetaInv{x}{y}{a}{b}$ + & $\displaystyle \GenRegIncBetaInv{x}{y}{a}{b}$ + \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Error Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Error Functions} +\index{Error Functions!Inverse} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Error Functions +% Error Function +\idxc{Erf}\verb|{x}| & $\Erf{x}$ & $\displaystyle \Erf{x}$ \\ +% Inverse of Error Function +%\ArcErf +\idxc{InvErf}\verb|{x}| & $\ErfInv{x}$ & $\displaystyle \ErfInv{x}$ \\ +% Generalized Error Function +\idxc{GenErf}\verb|{x}|{y} & $\GenErf{x}{y}$ & $\displaystyle \GenErf{x}{y}$ \\ +% Inverse of Generalized Error Function +%\ArcGenErf +\idxc{GenErfInv}\verb|{x}{y}| & $\GenErfInv{x}{y}$ & $\displaystyle \GenErfInv{x}{y}$ \\ +% Complimentary Error Function +\idxc{Erfc}\verb|{x}| & $\Erfc{x}$ & $\displaystyle \Erfc{x}$ \\ +% Inverse of Complimentary Error Function +% \ArcErfc +\idxc{ErfcInv}\verb|{x}| & $\ErfcInv{x}$ & $\displaystyle \ErfcInv{x}$ \\ +% Imaginary Error Function +\idxc{Erfi}\verb|{x}| & $\Erfi{x}$ & $\displaystyle \Erfi{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Fresnel Integrals} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Fresnel Integrals} +\index{Integrals!Fresnel} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Fresnel +\idxc{FresnelS}\verb|{x}| & $\FresnelS{x}$ & $\displaystyle \FresnelS{x}$ \\ +\idxc{FresnelC}\verb|{x}| & $\FresnelC{x}$ & $\displaystyle \FresnelC{x}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Exponential Integrals} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Exponential Integrals} +\index{Integrals!Exponential} + +\begin{center} +\begin{tabular}{ccc} +%%%%%% Exponential Integrals +% Exponential Integral E_\nu (x) +\idxc{ExpIntE}\verb|{\nu}{x}| & $\ExpIntE{\nu}{x}$ & $\displaystyle \ExpIntE{\nu}{x}$ \\ +% Exponential Integral Ei(x) +\idxc{ExpIntEi}\verb|{x}| & $\ExpIntEi{x}$ & $\displaystyle \ExpIntEi{x}$ \\ +% Logarithmic Integral li(x) +\idxc{LogInt}\verb|{x}| & $\LogInt{x}$ & $\displaystyle \LogInt{x}$ \\ +% Sine Integral +\idxc{SinInt}\verb|{x}| & $\SinInt{x}$ & $\displaystyle \SinInt{x}$ \\ +% Cosine Integral +\idxc{CosInt}\verb|{x}| & $\CosInt{x}$ & $\displaystyle \CosInt{x}$ \\ +% Hyperbolic Sine Integral +\idxc{SinhInt}\verb|{x}| & $\SinhInt{x}$ & $\displaystyle \SinhInt{x}$ \\ +% Hyperbolic Cosine Integral +\idxc{CoshInt}\verb|{x}| & $\CoshInt{x}$ & $\displaystyle \CoshInt{x}$ \\ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Hypergeometric Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Hypergeometric Function} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Hypergeometric Functions} + +\begin{center} +\begin{tabular}{c} +\idxc{Hypergeometric}\verb|{0}{0}{}{}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{0}{0}{}{}{x}$ & $\displaystyle \Hypergeometric{0}{0}{}{}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{0}{1}{}{b}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{0}{1}{}{b}{x}$ & $\displaystyle \Hypergeometric{0}{1}{}{b}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{1}{1}{a}{b}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{1}{1}{a}{b}{x}$ & $\displaystyle \Hypergeometric{1}{1}{a}{b}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{1}{1}{1}{1}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{1}{1}{1}{1}{x}$ & $\displaystyle \Hypergeometric{1}{1}{1}{1}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{3}{5}{a}{b}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{3}{5}{a}{b}{x}$ & $\displaystyle \Hypergeometric{3}{5}{a}{b}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{3}{5}{1,2,3}{1,2,3,4,5}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{3}{5}{1,2,3}{1,2,3,4,5}{x}$ & $\displaystyle \Hypergeometric{3}{5}{1,2,3}{1,2,3,4,5}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{p}{5}{a}{b}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{p}{5}{a}{b}{x}$ & $\displaystyle \Hypergeometric{p}{5}{a}{b}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{p}{3}{a}{1,2,3}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{p}{3}{a}{1,2,3}{x}$ $\displaystyle \Hypergeometric{p}{3}{a}{1,2,3}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{Hypergeometric}\verb|{p}{q}{a}{b}{x}| +\\ + \begin{tabular}{cc} + $\Hypergeometric{p}{q}{a}{b}{x}$ & $\displaystyle \Hypergeometric{p}{q}{a}{b}{x}$ \\ + + \end{tabular} +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Regularized Hypergeometric Function} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Hypergeometric Functions!Regularized} + +\begin{center} +\begin{tabular}{c} +\idxc{RegHypergeometric}\verb|{0}{0}{}{}{x}| +\\ + \begin{tabular}{cc} + $\RegHypergeometric{0}{0}{}{}{x}$ & $\displaystyle \RegHypergeometric{0}{0}{}{}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{RegHypergeometric}\verb|{0}{1}{}{b}{x}| +\\ + \begin{tabular}{cc} + $\RegHypergeometric{0}{1}{}{b}{x}$ & $\displaystyle \RegHypergeometric{0}{1}{}{b}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{RegHypergeometric}\verb|{3}{5}{a}{b}{x}| +\\ + \begin{tabular}{cc} + $\RegHypergeometric{3}{5}{a}{b}{x}$ & $\displaystyle \RegHypergeometric{3}{5}{a}{b}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{RegHypergeometric}\verb|{3}{5}{1,2,3}{1,2,3,4,5}{x}| +\\ + \begin{tabular}{cc} + $\RegHypergeometric{3}{5}{1,2,3}{1,2,3,4,5}{x}$ & $\displaystyle \RegHypergeometric{3}{5}{1,2,3}{1,2,3,4,5}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{RegHypergeometric}\verb|{p}{5}{a}{b}{x}| +\\ + \begin{tabular}{cc} + $\RegHypergeometric{p}{5}{a}{b}{x}$ & $\displaystyle \RegHypergeometric{p}{5}{a}{b}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{RegHypergeometric}\verb|{p}{3}{a}{1,2,3}{x}| +\\ + \begin{tabular}{cc} + $\RegHypergeometric{p}{3}{a}{1,2,3}{x}$ & $\displaystyle \RegHypergeometric{p}{3}{a}{1,2,3}{x}$ \\ + \end{tabular} +\\ +\\ +\idxc{RegHypergeometric}\verb|{p}{q}{a}{b}{x}| +\\ + \begin{tabular}{cc} + $\RegHypergeometric{p}{q}{a}{b}{x}$ & $\displaystyle \RegHypergeometric{p}{q}{a}{b}{x}$ \\ + + \end{tabular} +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Meijer G-Function} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Meijer G-Function} +\index{G-Function} + +\begin{center} +\begin{tabular}{c} +\idxc{MeijerG}\verb|[a,b]{n}{p}{m}{q}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a,b]{n}{p}{m}{q}{x}$ + & $\displaystyle \MeijerG[a,b]{n}{p}{m}{q}{x}$ + \end{tabular} +\\ +\end{tabular} + +\vspace{0.5cm} + +\begin{tabular}{c} +\idxc{MeijerG}\verb|{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}$ + & $\displaystyle \MeijerG{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}$ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[a,b]{4}{6}{3}{8}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a,b]{4}{6}{3}{8}{x}$ + & $\displaystyle \MeijerG[a,b]{4}{6}{3}{8}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[a,b]{4}{p}{3}{8}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a,b]{4}{p}{3}{8}{x}$ + & $\displaystyle \MeijerG[a,b]{4}{p}{3}{8}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[a,b]{n}{p}{3}{8}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a,b]{n}{p}{3}{8}{x}$ + & $\displaystyle \MeijerG[a,b]{n}{p}{3}{8}{x}$ + \\ + \end{tabular} +\\ +\end{tabular} + +\begin{tabular}{c} +\idxc{MeijerG}\verb|[a]{4}{6}{3,6,9}{12,15,18,21,24}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a]{4}{6}{3,6,9}{12,15,18,21,24}{x}$ + & $\displaystyle \MeijerG[a]{4}{6}{3,6,9}{12,15,18,21,24}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[a]{4}{p}{3,6,9}{12,15,18,21,24}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a]{4}{p}{3,6,9}{12,15,18,21,24}{x}$ + & $\displaystyle \MeijerG[a]{4}{p}{3,6,9}{12,15,18,21,24}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[a]{n}{6}{3,6,9}{12,15,18,21,24}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a]{n}{6}{3,6,9}{12,15,18,21,24}{x}$ + & $\displaystyle \MeijerG[a]{n}{6}{3,6,9}{12,15,18,21,24}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[a]{n}{p}{3,6,9}{12,15,18,21,24}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a]{n}{p}{3,6,9}{12,15,18,21,24}{x}$ + & $\displaystyle \MeijerG[a]{n}{p}{3,6,9}{12,15,18,21,24}{x}$ + \\ + \end{tabular} +\\ +\end{tabular} + +\begin{tabular}{c} +\idxc{MeijerG}\verb|[,b]{1,2,3,4}{5,6}{3}{8}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[,b]{1,2,3,4}{5,6}{3}{8}{x}$ + & $\displaystyle \MeijerG[,b]{1,2,3,4}{5,6}{3}{8}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[,b]{1,2,3,4}{5,6}{3}{q}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[,b]{1,2,3,4}{5,6}{3}{q}{x}$ + & $\displaystyle \MeijerG[,b]{1,2,3,4}{5,6}{3}{q}{x}$ + \\ + \end{tabular} +\\ +\\ +\idxc{MeijerG}\verb|[,b]{1,2,3,4}{5,6}{m}{q}{x}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[,b]{1,2,3,4}{5,6}{m}{q}{x}$ + & $\displaystyle \MeijerG[,b]{1,2,3,4}{5,6}{m}{q}{x}$ + \\ + \end{tabular} +\\ +\\ +\end{tabular} + +\index{Generalized Meijer G-Function} +\index{Meijer G-Function!Generalized} + +\begin{tabular}{c} +\idxc{MeijerG}\verb|[a,b]{n}{p}{m}{q}{x, r}| \vspace{0.10cm} +\\ + \begin{tabular}{cc} + $\MeijerG[a,b]{n}{p}{m}{q}{x, r}$ + & $\displaystyle \MeijerG[a,b]{n}{p}{m}{q}{x, r}$ + \end{tabular} +\\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Appell Hypergeometric Function $F_1$} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Appell Hypergeometric Function} +\index{Hypergeometric Functions!Appell} + +\begin{center} +\begin{tabular}{c} +\idxc{AppellFOne}\verb|{a}{b_1, b_2}{c}{x, y}| +\\ + \begin{tabular}{cc} + $\AppellFOne{a}{b_1,b_2}{c}{x,y}$ & $\displaystyle \AppellFOne{a}{b_1, b_2}{c}{x, y}$ \\ + \end{tabular} +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Tricomi Confluent Hypergeometric Function} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Tricomi Confluent Hypergeometric Function} +\index{Hypergeometric Functions!Tricomi Confluent} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +\idxc{HypergeometricU}\verb|{a}{b}{x}| + & $\HypergeometricU{a}{b}{x}$ + & $\displaystyle \HypergeometricU{a}{b}{x}$ \\ +\end{tabular} +\end{center} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Angular Momentum Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Clebsch-Gordon Coefficients} +\index{6-j Symbol} +\index{Six-j Symbol@6-j Symbol} +\index{Racah 6-j Symbol} +\index{3-j Symbol} +\index{Three-j Symbol@3-j Symbol} +\index{Wigner 3-j Symbol} + + +\begin{center} +\begin{tabular}{c} +\idxc{ClebschGordon}\verb|{j_1,m_1}{j_2,m_2}{j,m}| +\\ + \begin{tabular}{cc} + $\ClebschGordon{j_1, m_1}{j_2, m_2}{j, m}$ & $\displaystyle \ClebschGordon{j_1, m_1}{j_2, m_2}{j, m}$ + \\ + \end{tabular} +\\ +\\ +\idxc{SixJSymbol}\verb|{j_1,j_2,j_3}{j_4,j_5,j_6}| +\\ + \begin{tabular}{cc} + $\SixJSymbol{j_1,j_2,j_3}{j_4,j_5,j_6}$ & $\displaystyle \SixJSymbol{j_1,j_2,j_3}{j_4,j_5,j_6}$ + \\ + \end{tabular} +\\ +\\ +\idxc{ThreeJSymbol}\verb|{j_1,m_1}{j_2,m_2}{j_3,m_3}| +\\ + \begin{tabular}{cc} + $\ThreeJSymbol{j_1,m_1}{j_2,m_2}{j_3,m_3}$ & $\displaystyle \ThreeJSymbol{j_1,m_1}{j_2,m_2}{j_3,m_3}$ + \\ + \end{tabular} +\end{tabular} +\end{center} + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Elliptic Integrals} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Elliptic!Integrals} +\index{Integrals!Elliptic} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Complete Elliptic Integrals} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Complete Elliptic Integrals} +\index{Integrals!Elliptic!Complete} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Complete Elliptic Integrals +% Complete Elliptic Integral of the First Kind +\idxc{EllipticK}\verb|{x}| & $\EllipticK{x}$ & $\displaystyle \EllipticK{x}$ \\ +% Complete Elliptic Integral of the Second Kind +\idxc{EllipticE}\verb|{x}| & $\EllipticE{x}$ & $\displaystyle \EllipticE{x}$ \\ +% Complete Elliptic Integral of the Third Kind +\idxc{EllipticPi}\verb|{n,m}| & $\EllipticPi{n,m}$ & $\displaystyle \EllipticPi{n,m}$ \\ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Incomplete Elliptic Integrals} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Incomplete Elliptic Integrals} +\index{Integrals!Elliptic!Incomplete} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Incomplete Elliptic Integrals +% Incomplete Elliptic Integral of the First Kind +\idxc{IncEllipticF}\verb|{x}{m}| & $\IncEllipticF{x}{m}$ & $\displaystyle \IncEllipticF{x}{m}$ \\ +% Incomplete Elliptic Integral of the Second Kind +\idxc{IncEllipticE}\verb|{x}{m}| & $\IncEllipticE{x}{m}$ & $\displaystyle \IncEllipticE{x}{m}$ \\ +% Complete Elliptic Integral of the Third Kind +\idxc{IncEllipticPi}\verb|{n}{x}{m}| + & $\IncEllipticPi{n}{x}{m}$ + & $\displaystyle \IncEllipticPi{n}{x}{m}$ + \\ +\idxc{JacobiZeta}\verb|{x}{m}| & $\JacobiZeta{x}{m}$ & $\displaystyle \JacobiZeta{x}{m}$ \\ +\end{tabular} +\end{center} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Elliptic Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Elliptic!Functions} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Jacobi Theta Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Theta Functions!Jacobi} +\index{Jacobi Theta Functions} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Jacobi Theta Functions +% Jacobi Theta 1 .. 4 +\idxc{EllipticTheta}\verb|{1}{x}{q}| + & $\EllipticTheta{1}{x}{q}$ + & $\displaystyle \EllipticTheta{1}{x}{q}$ + \\ +% Jacobi Theta 1 ... 4 (Alternate Notation) +\idxc{JacobiTheta}\verb|{1}{x}{q}| & $\JacobiTheta{1}{x}{q}$ + & $\displaystyle \JacobiTheta{1}{x}{q}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Neville Theta Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Theta Functions!Neville} +\index{Neville Theta Functions} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Neville Theta Functions +% Neville Theta D +\idxc{NevilleThetaC}\verb|{x}{m}| & $\NevilleThetaC{x}{m}$ + & $\displaystyle \NevilleThetaC{x}{m}$ \\ +\idxc{NevilleThetaD}\verb|{x}{m}| & $\NevilleThetaD{x}{m}$ + & $\displaystyle \NevilleThetaD{x}{m}$ \\ +\idxc{NevilleThetaN}\verb|{x}{m}| & $\NevilleThetaN{x}{m}$ + & $\displaystyle \NevilleThetaN{x}{m}$ \\ +\idxc{NevilleThetaS}\verb|{x}{m}| & $\NevilleThetaS{x}{m}$ + & $\displaystyle \NevilleThetaS{x}{m}$ \\ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Weierstrass Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Weierstrass Functions} + +\begin{center} +\begin{tabular}{c} +%%%%%% Weierstrass Functions +\idxc{WeierstrassP}\verb|{z}{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassP{z}{g_2,g_3}$ & $\displaystyle \WeierstrassP{z}{g_2,g_3}$ \\ + \end{tabular} +\\ +\\ +\idxc{WeierstrassPInv}\verb|{z}{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassPInv{z}{g_2,g_3}$ & $\displaystyle \WeierstrassPInv{z}{g_2,g_3}$ \\ + \end{tabular} +\\ +\\ +\idxc{WeierstrassPGenInv}\verb|{z_1}{z_2}{g_2}{g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassPGenInv{z_1}{z_2}{g_2}{g_3}$ + & $\displaystyle \WeierstrassPGenInv{z_1}{z_2}{g_2}{g_3}$ + \\ + \end{tabular} +\\ +\\ +\idxc{WeierstrassSigma}\verb|{z}{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassSigma{z}{g_2,g_3}$ & $\displaystyle \WeierstrassSigma{z}{g_2,g_3}$ \\ + \end{tabular} +\\ +\\ +\idxc{AssocWeierstrassSigma}\verb|{n}{z}{g_2}{g_3}| +\\ +\idxc{WeiSigma}\verb|{n,z}{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\AssocWeierstrassSigma{n}{z}{g_2}{g_3}$ + & $\displaystyle \WeiSigma{n,z}{g_2,g_3}$ + \\ + \end{tabular} +\\ +\\ +\idxc{WeierstrassZeta}\verb|{z}{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassZeta{z}{g_2,g_3}$ & $\displaystyle \WeierstrassZeta{z}{g_2,g_3}$ \\ + \end{tabular} +\\ +\\ +\idxc{WeierstrassHalfPeriods}\verb|{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassHalfPeriods{g_2,g_3}$ & $\displaystyle \WeierstrassHalfPeriods{g_2,g_3}$ \\ + \end{tabular} +\\ +\\ +\idxc{WeierstrassInvariants}\verb|{\omega_1,\omega_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassInvariants{\omega_1,\omega_3}$ + & $\displaystyle \WeierstrassInvariants{\omega_1,\omega_3}$ + \\ + \end{tabular} +\\ +\end{tabular} + +\vspace{1.0cm} + +\begin{tabular}{c} +\verb|\Style{WeierstrassPHalfPeriodValuesDisplay=sf}| (Default)% +\Style{WeierstrassPHalfPeriodValuesDisplay=sf} +\\ +\idxc{WeierstrassPHalfPeriodValues}\verb|{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassPHalfPeriodValues{g_2,g_3}$ + & $\displaystyle \WeierstrassPHalfPeriodValues{g_2,g_3}$ + \\ + \end{tabular} +\\ +\\ +\\ +\verb|\Style{WeierstrassPHalfPeriodValuesDisplay=ff}|% +\Style{WeierstrassPHalfPeriodValuesDisplay=ff} +\\ +\idxc{WeierstrassPHalfPeriodValues}\verb|{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassPHalfPeriodValues{g_2,g_3}$ + & $\displaystyle \WeierstrassPHalfPeriodValues{g_2,g_3}$ + \\ + \end{tabular} +\\ +\end{tabular} + +\vspace{1cm} + +\begin{tabular}{c} +\verb|\Style{WeierstrassZetaHalfPeriodValuesDisplay=sf}| (Default)% +\Style{WeierstrassZetaHalfPeriodValuesDisplay=sf} +\\ +\idxc{WeierstrassZetaHalfPeriodValues}\verb|{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassZetaHalfPeriodValues{g_2,g_3}$ + & $\displaystyle \WeierstrassZetaHalfPeriodValues{g_2,g_3}$ + \\ + \end{tabular} +\\ +\\ +\\ +\verb|\Style{WeierstrassZetaHalfPeriodValuesDisplay=ff}|% +\Style{WeierstrassZetaHalfPeriodValuesDisplay=ff} +\\ +\idxc{WeierstrassZetaHalfPeriodValues}\verb|{g_2,g_3}| +\\ + \begin{tabular}{cc} + $\WeierstrassZetaHalfPeriodValues{g_2,g_3}$ + & $\displaystyle \WeierstrassZetaHalfPeriodValues{g_2,g_3}$ + \\ + \end{tabular} +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Jacobi Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Jacobi Functions} +\index{Jacobi Functions!Inverse} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Jacobi Functions +% am(z | m) +\idxc{JacobiAmplitude}\verb|{z}{m}| & $\JacobiAmplitude{z}{m}$ + & $\displaystyle \JacobiAmplitude{z}{m}$ + \\ +% cd(z | m) +\idxc{JacobiCD}\verb|{z}{m}| & $\JacobiCD{z}{m}$ & $\displaystyle \JacobiCD{z}{m}$ \\ +\idxc{JacobiCDInv}\verb|{z}{m}| & $\JacobiCDInv{z}{m}$ & $\displaystyle \JacobiCDInv{z}{m}$ \\ +% cn(z | m) +\idxc{JacobiCN}\verb|{z}{m}| & $\JacobiCN{z}{m}$ & $\displaystyle \JacobiCN{z}{m}$ \\ +\idxc{JacobiCNInv}\verb|{z}{m}| & $\JacobiCNInv{z}{m}$ & $\displaystyle \JacobiCNInv{z}{m}$ \\ +% cs(z | m) +\idxc{JacobiCS}\verb|{z}{m}| & $\JacobiCS{z}{m}$ & $\displaystyle \JacobiCS{z}{m}$ \\ +\idxc{JacobiCSInv}\verb|{z}{m}| & $\JacobiCSInv{z}{m}$ & $\displaystyle \JacobiCSInv{z}{m}$ \\ +% dc(z | m) +\idxc{JacobiDC}\verb|{z}{m}| & $\JacobiDC{z}{m}$ & $\displaystyle \JacobiDC{z}{m}$ \\ +\idxc{JacobiDCInv}\verb|{z}{m}| & $\JacobiDCInv{z}{m}$ & $\displaystyle \JacobiDCInv{z}{m}$ \\ +% dn(z | m) +\idxc{JacobiDN}\verb|{z}{m}| & $\JacobiDN{z}{m}$ & $\displaystyle \JacobiDN{z}{m}$ \\ +\idxc{JacobiDNInv}\verb|{z}{m}| & $\JacobiDNInv{z}{m}$ & $\displaystyle \JacobiDNInv{z}{m}$ \\ +% dn(z | m) +\idxc{JacobiDS}\verb|{z}{m}| & $\JacobiDS{z}{m}$ & $\displaystyle \JacobiDS{z}{m}$ \\ +\idxc{JacobiDSInv}\verb|{z}{m}| & $\JacobiDSInv{z}{m}$ & $\displaystyle \JacobiDSInv{z}{m}$ \\ +% nc(z | m) +\idxc{JacobiNC}\verb|{z}{m}| & $\JacobiNC{z}{m}$ & $\displaystyle \JacobiNC{z}{m}$ \\ +\idxc{JacobiNCInv}\verb|{z}{m}| & $\JacobiNCInv{z}{m}$ & $\displaystyle \JacobiNCInv{z}{m}$ \\ +% nd(z | m) +\idxc{JacobiND}\verb|{z}{m}| & $\JacobiND{z}{m}$ & $\displaystyle \JacobiND{z}{m}$ \\ +\idxc{JacobiNDInv}\verb|{z}{m}| & $\JacobiNDInv{z}{m}$ & $\displaystyle \JacobiNDInv{z}{m}$ \\ +% ns(z | m) +\idxc{JacobiNS}\verb|{z}{m}| & $\JacobiNS{z}{m}$ & $\displaystyle \JacobiNS{z}{m}$ \\ +\idxc{JacobiNSInv}\verb|{z}{m}| & $\JacobiNSInv{z}{m}$ & $\displaystyle \JacobiNSInv{z}{m}$ \\ +% sc(z | m) +\idxc{JacobiSC}\verb|{z}{m}| & $\JacobiSC{z}{m}$ & $\displaystyle \JacobiSC{z}{m}$ \\ +\idxc{JacobiSCInv}\verb|{z}{m}| & $\JacobiSCInv{z}{m}$ & $\displaystyle \JacobiSCInv{z}{m}$ \\ +% sd(z | m) +\idxc{JacobiSD}\verb|{z}{m}| & $\JacobiSD{z}{m}$ & $\displaystyle \JacobiSD{z}{m}$ \\ +\idxc{JacobiSDInv}\verb|{z}{m}| & $\JacobiSDInv{z}{m}$ & $\displaystyle \JacobiSDInv{z}{m}$ \\ +% sn(z | m) +\idxc{JacobiSN}\verb|{z}{m}| & $\JacobiSN{z}{m}$ & $\displaystyle \JacobiSN{z}{m}$ \\ +\idxc{JacobiSNInv}\verb|{z}{m}| & $\JacobiSNInv{z}{m}$ & $\displaystyle \JacobiSNInv{z}{m}$ \\ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Modular Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Modular Functions} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Modular Functions +\idxc{DedekindEta}\verb|{z}| & $\DedekindEta{z}$ & $\displaystyle \DedekindEta{z}$ \\ +\idxc{KleinInvariantJ}\verb|{z}| & $\KleinInvariantJ{z}$ & $\displaystyle \KleinInvariantJ{z}$ \\ +\idxc{ModularLambda}\verb|{z}| & $\ModularLambda{z}$ & $\displaystyle \ModularLambda{z}$ \\ +\idxc{EllipticNomeQ}\verb|{z}| & $\EllipticNomeQ{z}$ & $\displaystyle \EllipticNomeQ{z}$ \\ +\idxc{EllipticNomeQInv}\verb|{z}| & $\EllipticNomeQInv{z}$ + & $\displaystyle \EllipticNomeQInv{z}$ \\ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Arithmetic Geometric Mean} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Arithmetic Geometric Mean} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Arithmetic Geometric Mean +\idxc{ArithGeoMean}\verb|{a}{b}| & $\ArithGeoMean{a}{b}$ & $\displaystyle \ArithGeoMean{a}{b}$ \\ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Elliptic Exp and Log} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Elliptic!Exponential} +\index{Elliptic!Logarithm} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Elliptic Exp and Log +\idxc{EllipticExp}\verb|{x}{a,b}| & $\EllipticExp{x}{a,b}$ + & $\displaystyle \EllipticExp{x}{a,b}$ \\ +% elog(z_1, z_2; a,b) +\idxc{EllipticLog}\verb|{x,y}{a,b}| + & $\EllipticLog{x,y}{a,b}$ + & $\displaystyle \EllipticLog{x,y}{a,b}$ + \\ +\end{tabular} +\end{center} + + + + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Zeta Functions and Polylogarithms} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Zeta!Functions} +\index{Polylogarithm} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Zeta Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Zeta!Riemann} +\index{Zeta!Hurwitz} +\index{Zeta} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Riemann Zeta Function +\idxc{RiemannZeta}\verb|{s}| & $\RiemannZeta{s}$ & $\displaystyle \RiemannZeta{s}$ \\ +\idxc{Zeta}\verb|{s}| & $\Zeta{s}$ & $\displaystyle \Zeta{s}$ \\ + \\ +%%%%%% Hurwitz Zeta Function +\idxc{HurwitzZeta}\verb|{s}{a}| & $\HurwitzZeta{s}{a}$ & $\displaystyle \HurwitzZeta{s}{a}$ \\ +\idxc{Zeta}\verb|{s,a}| & $\Zeta{s,a}$ & $\displaystyle \Zeta{s,a}$ \\ + \\ +%%%%%% Riemann-Siegel Theta Function +\idxc{RiemannSiegelTheta}\verb|{x}| + & $\RiemannSiegelTheta{x}$ & $\displaystyle \RiemannSiegelTheta{x}$ \\ +%%%%%% Riemann-Siegel Z Function +\idxc{RiemannSiegelZ}\verb|{x}| & $\RiemannSiegelZ{x}$ & $\displaystyle \RiemannSiegelZ{x}$ \\ +%%%%%% Stieltjes Constant [\gamma_n] +\idxc{StieltjesGamma}\verb|{n}| & $\StieltjesGamma{n}$ & $\displaystyle \StieltjesGamma{n}$ \\ +%%%%%% Lerch transcendent [\Phi(z,s,a)] +\idxc{LerchPhi}\verb|{z}{s}{a}| & $\LerchPhi{z}{s}{a}$ & $\displaystyle \LerchPhi{z}{s}{a}$ \\ + \\ +%%%%%% Nielsen Polylogarithm [S_\nu^p(z)] +\idxc{NielsenPolyLog}\verb|{\nu}{p}{z}| + & $\NielsenPolyLog{\nu}{p}{z}$ & $\displaystyle \NielsenPolyLog{\nu}{p}{z}$ \\ +\idxc{PolyLog}\verb|{\nu,p,z}| & $\PolyLog{\nu,p,z}$ & $\displaystyle \PolyLog{\nu,p,z}$ \\ + \\ +%%%%%% Polylogarithm [Li_\nu (z)] +\idxc{PolyLog}\verb|{\nu,z}| & $\PolyLog{\nu,z}$ & $\displaystyle \PolyLog{\nu,z}$ \\ +%%%%%% Dilogarithm [\PolyLog{2,x}] +\idxc{DiLog}\verb|{z}| & $\DiLog{z}$ & $\displaystyle \DiLog{z}$ \\ +\end{tabular} +\end{center} + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Mathieu Functions and Characteristics} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Mathieu!Functions} +\index{Mathieu!Characteristics} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Mathieu Functions} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Mathieu Functions +%%%%%%%% Even Mathieu Function Ce(a,q,z) +\idxc{MathieuC}\verb|{a}{q}{z}| & $\MathieuC{a}{q}{z}$ & $\displaystyle \MathieuC{a}{q}{z}$ \\ +%%%%%%%% Odd Mathieu Function Se(a,q,z) +\idxc{MathieuS}\verb|{a}{q}{z}| & $\MathieuS{a}{q}{z}$ & $\displaystyle \MathieuS{a}{q}{z}$ \\ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Mathieu Characteristics} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Mathieu Characteristics +%%%%%%%% Characteristic Value of Even Mathieu Fucntion a_r(q) +\idxc{MathieuCharacteristicA}\verb|{r}{q}| + & $\MathieuCharacteristicA{r}{q}$ & $\displaystyle \MathieuCharacteristicA{r}{q}$ \\ +\idxc{MathieuCharisticA}\verb|{r}{q}| + & $\MathieuCharisticA{r}{q}$ & $\displaystyle \MathieuCharisticA{r}{q}$ \\ + \\ +%%%%%%%% Characteristic Value of Even Mathieu Fucntion b_r(q) +\idxc{MathieuCharacteristicB}\verb|{r}{q}| + & $\MathieuCharacteristicB{r}{q}$ & $\displaystyle \MathieuCharacteristicB{r}{q}$ \\ +\idxc{MathieuCharisticB}\verb|{r}{q}| + & $\MathieuCharisticB{r}{q}$ & $\displaystyle \MathieuCharisticB{r}{q}$ \\ + \\ +%%%%%%%% Characteristic Exponent of a Mathieu Fucntion r(a,q) +\idxc{MathieuCharacteristicExponent}\verb|{a}{q}| + & $\MathieuCharacteristicExponent{a}{q}$ + & $\displaystyle \MathieuCharacteristicExponent{a}{q}$ + \\ +\idxc{MathieuCharisticExp}\verb|{a}{q}| + & $\MathieuCharisticExp{a}{q}$ + & $\displaystyle \MathieuCharisticExp{a}{q}$ + \\ +\end{tabular} +\end{center} + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Complex Components} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Complex Components} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +\idxc{Abs}\verb|{z}| & $\Abs{z}$ & $\displaystyle \Abs{z}$ \\ +\idxc{Arg}\verb|{z}| & $\Arg{z}$ & $\displaystyle \Arg{z}$ \\ +\idxc{Conj}\verb|{z}| & $\Conj{z}$ & $\displaystyle \Conj{z}$ \\ +\Style{Conjugate=bar}% +\verb|\Style{Conjugate=bar}|% +\idxc{Conj}\verb|{z}| & $\Conj{z}$ & $\displaystyle \Conj{z}$ \\ +\Style{Conjugate=overline}% +\verb|\Style{Conjugate=overline}|% +\idxc{Conj}\verb|{z}| & $\Conj{z}$ & $\displaystyle \Conj{z}$ \\ +\idxc{Real}\verb|{z}| & $\Real{z}$ & $\displaystyle \Real{z}$ \\ +\idxc{Imag}\verb|{z}| & $\Imag{z}$ & $\displaystyle \Imag{z}$ \\ +\idxc{Sign}\verb|{z}| & $\Sign{z}$ & $\displaystyle \Sign{z}$ \\ +\end{tabular} +\end{center} + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Number Theory Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Number Theory} +\index{Functions!Number Theory} +\index{Totient Function} +\index{Euler Totient Function} +\index{Moebius Function} +\index{Jacobi!Symbol} +\index{Symbol!Jacobi} +\index{Charmicheal Lambda Function} +\index{Lambda Function!Charmicheal} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +\idxc{FactorInteger}\verb|{n}| & $\FactorInteger{n}$ & $\displaystyle \FactorInteger{n}$ \\ +\idxc{Factors}\verb|{n}| & $\Factors{n}$ & $\displaystyle \Factors{n}$ \\ + \\ +%%%%%% Divisors +\idxc{Divisors}\verb|{n}| & $\Divisors{n}$ & $\displaystyle \Divisors{n}$ \\ +%%%%%% Prime +\idxc{Prime}\verb|{n}| & $\Prime{n}$ & $\displaystyle \Prime{n}$ \\ +%%%%%% pi(x) +\idxc{PrimePi}\verb|{x}| & $\PrimePi{x}$ & $\displaystyle \PrimePi{x}$ \\ +%%%%%% Sum of divisor powers \DivisorSigma{k}{n} +\idxc{DivisorSigma}\verb|{k}{n}| & $\DivisorSigma{k}{n}$ & $\displaystyle \DivisorSigma{k}{n}$ \\ +%%%%%% Euler Totient Function +\idxc{EulerPhi}\verb|{n}| & $\EulerPhi{n}$ & $\displaystyle \EulerPhi{n}$ \\ +%%%%%% Moebius Function +\idxc{MoebiusMu}\verb|{n}| & $\MoebiusMu{n}$ & $\displaystyle \MoebiusMu{n}$ \\ +%%%%%% Jacobi Symbol \JacobiSymbol{n}{m} +\idxc{JacobiSymbol}\verb|{n}{m}| & $\JacobiSymbol{n}{m}$ & $\displaystyle \JacobiSymbol{n}{m}$ \\ + \\ +%%%%%% Carmichael Lambda Function +\idxc{CarmichaelLambda}\verb|{n}| & $\CarmichaelLambda{n}$ + & $\displaystyle \CarmichaelLambda{n}$ \\ +\end{tabular} + +\begin{tabular}{c} +\idxc{DigitCount}\verb|{n}{b}| +\\ + \begin{tabular}{cc} + {\bf Inline:} & $\DigitCount{n}{b}$ \\ + {\bf Display:} & $\displaystyle \DigitCount{n}{b}$ \\ + \end{tabular} +\\ +\\ +\idxc{DigitCount}\verb|{n}{6}| +\\ + \begin{tabular}{cc} + {\bf Inline:} & $\DigitCount{n}{6}$ \\ + {\bf Display:} & $\displaystyle \DigitCount{n}{6}$ \\ + \end{tabular} +\end{tabular} +\end{center} + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Generalized Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Generalized Functions} +\index{Functions!Generalized} +\index{Heaviside Step} +%\index{Functions!Heaviside Step} +\index{Unit Step} +%\index{Functions!Unit Step} + +\begin{center} +\begin{tabular}{ccc} +\headerRow +%%%%%% Dirac Delta Function +\idxc{DiracDelta}\verb|{x}| & $\DiracDelta{x}$ & $\displaystyle \DiracDelta{x}$ \\ +\idxc{DiracDelta}\verb|{x_1, x_2}| & $\DiracDelta{x_1, x_2}$ & $\displaystyle \DiracDelta{x_1, x_2}$ \\ + \\ +%%%%%% Heaviside Step Function +\idxc{HeavisideStep}\verb|{x}| & $\HeavisideStep{x}$ & $\displaystyle \HeavisideStep{x}$ \\ +\idxc{HeavisideStep}\verb|{x, y}| & $\HeavisideStep{x,y}$ & $\displaystyle \HeavisideStep{x,y}$ \\ +\idxc{UnitStep}\verb|{x}| & $\UnitStep{x}$ & $\displaystyle \UnitStep{x}$ \\ +\idxc{UnitStep}\verb|{x,y}| & $\UnitStep{x,y}$ & $\displaystyle \UnitStep{x,y}$ \\ +\end{tabular} +\end{center} + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\subsection{Calculus Functions} +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Calculus} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Derivatives} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Calculus!Derivatives} +\index{Derivatives!Total} +\index{Total Derivatives} + +\begin{center} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=inset,DShorten=true}| (Default)% +\Style{DDisplayFunc=inset,DShorten=true} \\ + \\ +\begin{tabular}{ccc} +\idxc{D}\verb|{f}{x}| & $\D{f}{x}$ & $\displaystyle \D{f}{x}$ \\ + \\ +\idxc{D}\verb|[n]{f}{x}| & $\D[n]{f}{x}$ & $\displaystyle \D[n]{f}{x}$ \\ + \\ +\end{tabular} +\end{tabular} + +\vspace{.5cm} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=outset,DShorten=false}|% +\Style{DDisplayFunc=outset,DShorten=false} \\ + \\ +\begin{tabular}{ccc} +\idxc{D}\verb|{f}{x}| & $\D{f}{x}$ & $\displaystyle \D{f}{x}$ \\ + \\ +\idxc{D}\verb|[n]{f}{x}| & $\D[n]{f}{x}$ & $\displaystyle \D[n]{f}{x}$ \\ + \\ +\idxc{D}\verb|{f}{x,y,z}| & $\D{f}{x,y,z}$ & $\displaystyle \D{f}{x,y,z}$ \\ + \\ +\idxc{D}\verb|[2,n,3]{f}{x,y,z}| & $\D[2,n,3]{f}{x,y,z}$ & $\displaystyle \D[2,n,3]{f}{x,y,z}$ + \\ + \\ +\idxc{D}\verb|[1,n,3]{f}{x,y,z}| & $\D[1,n,3]{f}{x,y,z}$ & $\displaystyle \D[1,n,3]{f}{x,y,z}$ + \\ +\end{tabular} +\end{tabular} + +\vspace{.5cm} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=outset,DShorten=true}|% +\Style{DDisplayFunc=outset,DShorten=true} \\ + \\ +\begin{tabular}{ccc} +\idxc{D}\verb|{f}{x}| & $\D{f}{x}$ & $\displaystyle \D{f}{x}$ \\ + \\ +\idxc{D}\verb|[n]{f}{x}| & $\D[n]{f}{x}$ & $\displaystyle \D[n]{f}{x}$ \\ + \\ +\idxc{D}\verb|{f}{x,y,z}| & $\D{f}{x,y,z}$ & $\displaystyle \D{f}{x,y,z}$ \\ + \\ +\idxc{D}\verb|[2,n,3]{f}{x,y,z}| & $\D[2,n,3]{f}{x,y,z}$ & $\displaystyle \D[2,n,3]{f}{x,y,z}$ + \\ + \\ +\idxc{D}\verb|[1,n,3]{f}{x,y,z}| & $\D[1,n,3]{f}{x,y,z}$ & $\displaystyle \D[1,n,3]{f}{x,y,z}$ + \\ +\end{tabular} +\end{tabular} + +\vspace{0.5cm} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=inset,DShorten=true}| +\Style{DDisplayFunc=inset,DShorten=true} \\ + \\ +\begin{tabular}{ccc} +\idxc{D}\verb|{f}{x}| & $\D{f}{x}$ & $\displaystyle \D{f}{x}$ \\ + \\ +\idxc{D}\verb|[n]{f}{x}| & $\D[n]{f}{x}$ & $\displaystyle \D[n]{f}{x}$ \\ + \\ +\idxc{D}\verb|{f}{x,y,z}| & $\D{f}{x,y,z}$ & $\displaystyle \D{f}{x,y,z}$ \\ + \\ +\idxc{D}\verb|[2,n,3]{f}{x,y,z}| & $\D[2,n,3]{f}{x,y,z}$ & $\displaystyle \D[2,n,3]{f}{x,y,z}$ + \\ + \\ +\idxc{D}\verb|[1,n,3]{f}{x,y,z}| & $\D[1,n,3]{f}{x,y,z}$ & $\displaystyle \D[1,n,3]{f}{x,y,z}$ +\end{tabular} +\end{tabular} + +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Partial Derivatives} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Calculus!Derivatives} +\index{Derivatives!Partial} +\index{Partial Derivatives} + +\begin{center} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=inset,DShorten=true}| (Default)% +\Style{DDisplayFunc=inset,DShorten=true} \\ + \\ +\begin{tabular}{ccc} +\idxc{pderiv}\verb|{f}{x}| & $\pderiv{f}{x}$ & $\displaystyle \pderiv{f}{x}$ \\ + \\ +\idxc{pderiv}\verb|[n]{f}{x}| & $\pderiv[n]{f}{x}$ & $\displaystyle \pderiv[n]{f}{x}$ \\ + \\ +\end{tabular} +\end{tabular} + +\vspace{.5cm} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=outset,DShorten=false}|% +\Style{DDisplayFunc=outset,DShorten=false} \\ + \\ +\begin{tabular}{ccc} +\idxc{pderiv}\verb|{f}{x}| & $\pderiv{f}{x}$ & $\displaystyle \pderiv{f}{x}$ \\ + \\ +\idxc{pderiv}\verb|[n]{f}{x}| & $\pderiv[n]{f}{x}$ & $\displaystyle \pderiv[n]{f}{x}$ \\ + \\ +\idxc{pderiv}\verb|{f}{x,y,z}| & $\pderiv{f}{x,y,z}$ & $\displaystyle \pderiv{f}{x,y,z}$ \\ + \\ +\idxc{pderiv}\verb|[2,n,3]{f}{x,y,z}| & $\pderiv[2,n,3]{f}{x,y,z}$ & $\displaystyle \pderiv[2,n,3]{f}{x,y,z}$ + \\ + \\ +\idxc{pderiv}\verb|[1,n,3]{f}{x,y,z}| & $\pderiv[1,n,3]{f}{x,y,z}$ & $\displaystyle \pderiv[1,n,3]{f}{x,y,z}$ + \\ +\end{tabular} +\end{tabular} + +\vspace{.5cm} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=outset,DShorten=true}|% +\Style{DDisplayFunc=outset,DShorten=true} \\ + \\ +\begin{tabular}{ccc} +\idxc{pderiv}\verb|{f}{x}| & $\pderiv{f}{x}$ & $\displaystyle \pderiv{f}{x}$ \\ + \\ +\idxc{pderiv}\verb|[n]{f}{x}| & $\pderiv[n]{f}{x}$ & $\displaystyle \pderiv[n]{f}{x}$ \\ + \\ +\idxc{pderiv}\verb|{f}{x,y,z}| & $\pderiv{f}{x,y,z}$ & $\displaystyle \pderiv{f}{x,y,z}$ \\ + \\ +\idxc{pderiv}\verb|[2,n,3]{f}{x,y,z}| & $\pderiv[2,n,3]{f}{x,y,z}$ & $\displaystyle \pderiv[2,n,3]{f}{x,y,z}$ + \\ + \\ +\idxc{pderiv}\verb|[1,n,3]{f}{x,y,z}| & $\pderiv[1,n,3]{f}{x,y,z}$ & $\displaystyle \pderiv[1,n,3]{f}{x,y,z}$ + \\ +\end{tabular} +\end{tabular} + +\vspace{0.5cm} + +\begin{tabular}{c} +\verb|\Style{DDisplayFunc=inset,DShorten=true}| +\Style{DDisplayFunc=inset,DShorten=true} \\ + \\ +\begin{tabular}{ccc} +\idxc{pderiv}\verb|{f}{x}| & $\pderiv{f}{x}$ & $\displaystyle \pderiv{f}{x}$ \\ + \\ +\idxc{pderiv}\verb|[n]{f}{x}| & $\pderiv[n]{f}{x}$ & $\displaystyle \pderiv[n]{f}{x}$ \\ + \\ +\idxc{pderiv}\verb|{f}{x,y,z}| & $\pderiv{f}{x,y,z}$ & $\displaystyle \pderiv{f}{x,y,z}$ \\ + \\ +\idxc{pderiv}\verb|[2,n,3]{f}{x,y,z}| & $\pderiv[2,n,3]{f}{x,y,z}$ & $\displaystyle \pderiv[2,n,3]{f}{x,y,z}$ + \\ + \\ +\idxc{pderiv}\verb|[1,n,3]{f}{x,y,z}| & $\pderiv[1,n,3]{f}{x,y,z}$ & $\displaystyle \pderiv[1,n,3]{f}{x,y,z}$ +\end{tabular} +\end{tabular} + +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Integrals} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Calculus!Integrals} +\index{Integrals} +\index{Integrals!Definite} +\index{Integrals!Indefinite} + +\begin{center} +\begin{tabular}{ccc} +\headerRow + \\ +\idxc{Integrate}\verb|{f}{x}| & $\Integrate{f}{x}$ & $\displaystyle \Integrate{f}{x}$ + \\ + \\ +\idxc{Int}\verb|{f(x)}{x}| & $\Int{f(x)}{x}$ & $\displaystyle \Int{f(x)}{x}$ \\ + \\ +\idxc{Int}\verb|{f}{S,C}| & $\Int{f}{S,C}$ & $\displaystyle \Int{f}{S,C}$ \\ + \\ +\idxc{Int}\verb|{f(x)}{x,a,b}| & $\Int{f(x)}{x,a,b}$ & $\displaystyle \Int{f(x)}{x,a,b}$ + \\ + \\ +\idxc{Int}\verb|{f(x)}{x,0,b}| & $\Int{f(x)}{x,0,b}$ & $\displaystyle \Int{f(x)}{x,0,b}$ + \\ +\idxc{Int}\verb|{\Int{f(x)}{x,0,y}}{y,0,z}| + & $\Int{ \Int{f(x)}{x,0,y} }{y,0,z}$ + & $\displaystyle \Int{ \Int{f(x)}{x,0,y} }{y,0,z}$ +\end{tabular} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Sums and Products} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\begin{tabular}{ccc} +\headerRow + \\ +\idxc{Sum}\verb|{a(k)}{k}| & $\Sum{a(k)}{k}$ & $\displaystyle \Sum{a(k)}{k}$ \\ + \\ +\idxc{Sum}\verb|{a(k)}{k,1,n}| & $\Sum{a(k)}{k,1,n}$ & $\displaystyle \Sum{a(k)}{k,1,n}$ + \\ + \\ +\idxc{Prod}\verb|{a(k)}{k}| & $\Prod{a(k)}{k}$ & $\displaystyle \Prod{a(k)}{k}$ + \\ + \\ +\idxc{Prod}\verb|{a(k)}{k,1,n}| & $\Prod{a(k)}{k,1,n}$ & $\displaystyle \Prod{a(k)}{k,1,n}$ +\end{tabular} +\end{center} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +\subsubsection{Matrices} +%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\index{Matrix!Identity} +\index{Matrices!Identity} + +\begin{center} +\begin{tabular}{ccc} +\headerRow \\ +\idxc{IdentityMatrix} & $\IdentityMatrix$ & $\displaystyle \IdentityMatrix$ \\ +\verb|\Style{IdentityMatrixParen=p}| (Default)% +\Style{IdentityMatrixParen=p} \\ +\idxc{IdentityMatrix[2]} & $\IdentityMatrix[2]$ & $\displaystyle \IdentityMatrix[2]$ \\ +\verb|\Style{IdentityMatrixParen=b}|% +\Style{IdentityMatrixParen=b} \\ +\idxc{IdentityMatrix[2]} & $\IdentityMatrix[2]$ & $\displaystyle \IdentityMatrix[2]$ \\ +\verb|\Style{IdentityMatrixParen=br}|% +\Style{IdentityMatrixParen=br} \\ +\idxc{IdentityMatrix[2]} & $\IdentityMatrix[2]$ & $\displaystyle \IdentityMatrix[2]$ \\ +\verb|\Style{IdentityMatrixParen=none}|% +\Style{IdentityMatrixParen=none} \\ +\idxc{IdentityMatrix[2]} & $\IdentityMatrix[2]$ & $\displaystyle \IdentityMatrix[2]$% +\Style{IdentityMatrixParen=p} \\ +\end{tabular} +\end{center} + +\idxc{IdentityMatrix}\verb|[20]| yields + +$$ +\IdentityMatrix[20] +$$ + +\printindex + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ REFERENCES ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]] +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%\newpage + +%\begin{thebibliography}{hello} +%\end{thebibliography} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ END REFERENCES ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]] +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\end{document} % End of document diff --git a/Master/texmf-dist/doc/latex/cool/README b/Master/texmf-dist/doc/latex/cool/README new file mode 100644 index 00000000000..9d5710e2993 --- /dev/null +++ b/Master/texmf-dist/doc/latex/cool/README @@ -0,0 +1,43 @@ +Description
+-----------
+
+The cool of the cool package stands for COntent Oriented LaTeX. It is designed
+to give LaTeX the power to retain mathematical meaning of its expressions in
+addition to the typsetting instructions.
+
+One advantage of keeping mathematical meaning is that conversion of LaTeX
+documents to other executable formats (such as Content MathML or Mathematica
+code) is greatly simplified.
+
+This package requires the following, non-standard LaTeX packages
+(all of which are available on www.ctan.org):
+
+* coolstr
+* coollist
+* forloop
+
+
+Installation
+------------
+
+To install this package, run cool.ins through LaTeX. This will generate
+a file called cool.sty. Put this file somewhere where LaTeX will find
+it---for instance localtexmf/tex/latex/cool/ (note that you will need
+to create the folder cool).
+
+If you are using MikTeX, you then need to refresh the file name database
+by using MikTeX Options
+
+
+License
+-------
+
+This pacakge is released under the Lesser GNU General Public License. See
+http://www.gnu.org/licenses/licenses.html#LGPL for more details.
+
+Contact
+-------
+
+Any bugs may be reported to the author by sending an email to the address with
+the first part being nsetzer, then an at sign, the next part is umd, and
+finally it ends in dot edu.
\ No newline at end of file diff --git a/Master/texmf-dist/doc/latex/cool/cool.pdf b/Master/texmf-dist/doc/latex/cool/cool.pdf Binary files differnew file mode 100644 index 00000000000..47917b2d216 --- /dev/null +++ b/Master/texmf-dist/doc/latex/cool/cool.pdf |