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\documentclass[11pt]{article}
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\usepackage{amscd}
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\textheight 260mm
\textwidth 160mm
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\def\hs{\hbox to 3mm{}}
\def\hhs{\hbox to 5cm{}}
\def\ss{\smallskip}
\def\ms{\smallskip}
\def\bs{\bigskip}
\def\bbss{\vskip 6mm}

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\def\pointir{\unskip . --- \ignorespaces}
\def\binomial#1#2{\left(\,\matrix{#1 \cr #2}\,\right)}
\def\NF{\mathcal{N}}
\def\si{\sigma}
\def\om{\omega}
\def\al{\alpha}
\def\ia{\rightarrow\hspace{-13pt}+\ }
\def\ca{\nearrow\hspace{-10pt}\searrow}
\def\cs{\rightarrow\hspace{-15pt}+\ }
\def\SGS{\bigoplus_{n\geq0}{\mathbb Q}[\SG_n]}
\def\FQSym{{\bf FQSym}}
\def\MQSym{{\bf MQSym}}
\def\Zy{\frak Z}
\def\F{\mathbf{F}}
\def\binomial#1#2{\begin{pmatrix} #1 \cr #2\end{pmatrix}}


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% Espaces
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\def\ncp#1#2{#1\langle #2 \rangle}
\def\ncs#1#2{#1\langle\langle #2 \rangle\rangle}
\def\G{\frak{G}}
\def\SG{\frak{S}}


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% Constantes
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\def\N{\mathbb{N}}
\def\Q{\mathbb{Q}}
\def\Z{\mathbb{Z}}
\def\p{\frak p}




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\newtheorem{example}{Example}[section]
\newtheorem{note}[example]{Note}
\newtheorem{theorem}[example]{Theorem}
\newtheorem{exercise}{Exercise}[section]
\newtheorem{corollary}[example]{Corollary}
\newtheorem{conjecture}[example]{Conjecture}
\newtheorem{definition}[example]{Definition}
\newtheorem{proposition}[example]{Proposition}
\newtheorem{algorithm}[example]{Algorithm}
\newtheorem{lemma}[example]{Lemma}
\def\mref#1{(\ref{#1})}
\def\Proof{\medskip\noindent {\it Proof --- \ }}
\def\cqfd{\hfill \\ \hbox{ }\hfill$\Box$ \bigskip}





\begin{document}

\begin{center}
\begin{tabular}{c|c|c|c}
Operator            & Substitution Factor   & Description\\
\hline
&&\\
$\left(1+(a^+)^2\right)a$   & $s_\lambda(x)=\displaystyle{\frac{xcos(\lambda)+sin(\lambda)}{cos(\lambda)-xsin(\lambda)}}$ &
One-parameter group \\
&& of homographies\\
&&\\
\hline
&&\\
$\displaystyle{\frac{\sqrt{1+(a^+)^2}}{a^+}}a$ &  $s_\lambda(x)=\sqrt{x^2+2\lambda\sqrt{1+x^2}+\lambda^2}$&
Composition of quadratic\\
&& direct and inverse functions\\
&&\\
\end{tabular}
\end{center}
\newpage

\begin{equation}
s_2(z)=e^{(e^{z}-1)}-1;\ s_3(z)=e^{(e^{(e^{z}-1)}-1)}-1;\ s_{-1}(z)=log(1+z)
\end{equation}

\begin{equation}
c_n=\binomial{2n}{n}
\end{equation}

\begin{equation}
\frac{(y\frac{d}{dx})^n}{n!} \frac{x^m}{m!}\big|_{x=0}=\delta_{mn} \frac{y^n}{n!}
\end{equation}

\begin{eqnarray}
\sum_{n,k}I(n,k) \frac{x^n}{n!}y^k=\sum_{n\geq 0}\sum_{k\leq n}\binomial{n}{k} k^{n-k} \frac{x^n}{n!}y^k=\cr
\sum_{k\leq n}\sum_{n\geq k}\binomial{n}{k} k^{n-k} \frac{x^{n-k}x^k}{n!}y^k=e^{yxe^x}                  
\end{eqnarray}


\end{document}