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\title{Content \LaTeXe} % Declares the document's title.
\author{N. Setzer} % Declares the author's name.
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%##########################################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.
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\section{Commands}
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\subsection{Constants}
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\subsubsection{}
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\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}
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\subsubsection{Symbols}
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\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}
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\subsection{}
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\subsubsection{Exponential and Logarithmic Functions}
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\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}
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\subsubsection{Trigonometric Functions}
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\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}
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\subsubsection{Inverse Trigonometric Functions}
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\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}
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\subsubsection{Hyberbolic Functions}
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\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}
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\subsubsection{Inverse Hyberbolic Functions}
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\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}
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\subsubsection{Product Logarithms}
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\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}
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\subsubsection{Max and Min}
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\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}
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\subsection{Bessel, Airy, and Struve Functions}
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\subsubsection{Bessel}
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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}
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\subsubsection{Airy}
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\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}
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\subsubsection{Struve}
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\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}
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\subsection{Integer Functions}
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\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}
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\subsubsection{}
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\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}
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\subsubsection{}
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\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}
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\subsubsection{}
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\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}
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\subsubsection{}
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\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}
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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
\subsection{Polynomials}
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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}
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\subsection{Gamma, Beta, and Error Functions}
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\subsubsection{Factorials}
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%%%% 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}
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\subsubsection{Gamma Functions}
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\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}
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\subsubsection{Derivatives of Gamma Functions}
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\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}
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\subsubsection{Error Functions}
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\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}
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\subsubsection{Fresnel Integrals}
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\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}
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\subsubsection{Exponential Integrals}
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\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}
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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
\subsection{Hypergeometric Functions}
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\subsubsection{Hypergeometric Function}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\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}
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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
\subsection{Mathieu Functions and Characteristics}
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\index{Mathieu!Functions}
\index{Mathieu!Characteristics}
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%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %
\subsubsection{Mathieu Functions}
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\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}
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%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %
\subsubsection{Mathieu Characteristics}
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\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}
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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
\subsection{Complex Components}
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\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}
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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
\subsection{Number Theory Functions}
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
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\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}
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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
\subsection{Generalized Functions}
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
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\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}
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\index{Calculus}
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%% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %% %
\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
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