%The following command print all the series and their expansion
%which are typeset in the first horizontal part of the page 10.
%
%The macro has one parameter.
% 1) The width to use to typeset the formulae
%
\newcommand\TTenSerieTwo[1]{%
%This command typeset a line equation about the series on page 10
%
%The command has 4 parameters
% 1) The first formula to be expanded
% 2) its expanded version
% 3) The second formula to be expanded
% 4) its expanded version
\def\LineOfArray##1##2##3##4{%
##1&=&##2&##3&=&##4\\[\TTenExpansionSkip]%
}%
\parbox[t]{#1}{%
\TTenSeriesFontSize
\TTenTitle{Expansions:}%
$\displaystyle
\begin{array}{l@{\hspace{.1em}}c@{\hspace{.2em}}ll@{\hspace{.1em}}c@{\hspace{.2em}}l}%
\LineOfArray{\frac{1}{(1-x)^{n+1}}\ln\frac{1}{1- x}}%
{\sum_{i=0}^\infty (H_{n+i} - H_n) \binom{n+i}{i} x^i}%
{\left(\frac{1}{x}\right)^{\overline{-n}}}%
{\sum_{i=0}^\infty \SousEnsemble{i}{n} x^i}%
\LineOfArray{x^{\overline{n}}}%
{\sum_{i=0}^\infty \Cycle{n}{i} x^i}%
{(e^x - 1)^n}%
{\sum_{i=0}^\infty \SousEnsemble{i}{n} \frac{n! x^i}{i!}}%
\LineOfArray{\left(\ln \frac{1}{1 -x}\right)^n}%
{\sum_{i=0}^\infty \Cycle{i}{n} \frac{n! x^i}{i!}}%
{x \cot x}%
{\sum_{i=0}^\infty \frac{(-4)^i B_{2i} x^{2i}}{(2i)!}}%
\LineOfArray{\tan x}%
{\sum_{i=1}^\infty (-1)^{i-1}\frac{2^{2i} (2^{2i} - 1) B_{2i} x^{2i-1}}{(2i)!}}%
{\zeta(x)}%
{\sum_{i=1}^\infty \frac{1}{i^x}}%
\LineOfArray{\frac{1}{\zeta(x)}}%
{\sum_{i=1}^\infty \frac{\mu(i)}{i^x}}%
{\frac{\zeta(x-1)}{\zeta(x)}}%
{\sum_{i=1}^\infty \frac{\phi(i)}{i^x}}%
\end{array}$%
}%
}
