\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