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%This command provides the text about the 'General' part
%of the page 3
%
%The command has one parameter:
% 1) The width of the text
\newcommand\TThreeGeneral[1]{%
\parbox[t]{#1}{%
\DisplaySpace{\TThreeDisplaySpace}{\TThreeDisplayShortSpace}
%Since the columns is narrow, ragged right looks nicer
%Don't use \RaggedRight here since the result is not good
\raggedright
\TThreeTitle{Bernoulli Numbers
(\MathRemark[\relax]{B_i = 0}, \MathRemark[\relax]{\text{odd} i \neq 1}):}%
\begin{DisplayFormulae}{1}{0pt}{5ex plus 1ex minus 1ex}{\SmallChar}{\StyleWithoutNumber}
\def\FmSep{\unskip\text{,}}
\Fm{B_0 = 1}
\Fm{B_1 = -{\frac{1}{2}}}
\Fm{B_2 = \frac{1}{6}}
\Fm{B_4 = -{\frac{1}{30}}}
\Fm{B_6 = \frac{1}{42}}
\Fm{B_8 = -{\frac{1}{30}}}
\def\FmSep{\relax}
\Fm{B_{10} = \frac{5}{66}}
\end{DisplayFormulae}
\TThreeTitle{Change of base, quadratic formula:}%
\begin{DisplayFormulae}{1}{0pt}{6ex plus 1ex minus 1ex}{\BigChar}{\StyleWithoutNumber}
\Fm{\log_b x = \frac{\log_a{x}}{\log_a{b}}},
\Fm{\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}
\end{DisplayFormulae}
\TThreeTitle{Euler's number $e$:}
\AdjustSpace{1.5ex plus .5ex minus .5ex}
\begin{DisplayFormulae}{1}{0pt}{4ex plus 1ex minus 1ex}{\BigChar}{\StyleWithoutNumber}
\def\FmSep{\unskip\text{,}}
\Fm{e = 1 + \tfrac{1}{2} + \tfrac{1}{6} + \tfrac{1}{24} + \cdots = \sum_{n=0}^\infty\frac{1}{n!}}
\Fm{\lim_{n \to \infty} \Bigl(1 + \frac{x}{n}\Bigr)^n = e^x}
\Fm{\left(1 + \tfrac{1}{n} \right)^n < e < \left(1 + \tfrac{1}{n} \right)^{n+1}}
\def\FmSep{\relax}
\def\FirstPart{\left(1 + \tfrac{1}{n} \right)^n = \mbox{}}
\FmPartA{\FirstPart e - \frac{e}{2 n} + \frac{11 e}{24 n^2} -}
\FmPartB{\FirstPart}{O\left(\frac{1}{n^3}\right)}
\end{DisplayFormulae}
\TThreeTitle{Harmonic numbers:}
\AdjustSpace{1.5ex plus .5ex minus .5ex}
\begin{DisplayFormulae}{1}{0pt}{5ex plus 1ex minus 1ex}{\BigChar}{\StyleWithoutNumber}
\def\FmSep{\unskip\text{,}}
\Fm{1}
\Fm{\frac{3}{2}}
\Fm{\frac{11}{6}}
\Fm{\frac{25}{12}}
\Fm{\frac{137}{60}}
\Fm{\frac{49}{20}}
\Fm{\frac{363}{140}}
\Fm{\frac{761}{280}}
\Fm{\frac{7129}{2520}}
\Fm{\ldots}
\Fm{\ln n < H_n < \ln n + 1}
\def\FmSep{\relax}
\Fm{H_n = \ln n + \gamma + O\bigg(\frac{1}{n} \bigg)}
\end{DisplayFormulae}
\TThreeTitle{Factorial, Stirling's approximation:}
\begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus 1ex}{\SmallChar}{\StyleWithoutNumber}
\def\FmSep{\unskip\text{,}}
\Fm{1}
\Fm{2}
\Fm{6}
\Fm{24}
\Fm{120}
\Fm{720}
\Fm{5040}
\Fm{40320}
\Fm{362880}
\def\FmSep{\relax}
\Fm{\ldots}
\Fm{n! = \sqrt{2\pi n} \bigg(\frac{n}{e}\bigg)^n\bigg(1 +
\Theta\bigg(\frac{1}{n}\bigg)\bigg)}
\end{DisplayFormulae}
\TThreeTitle{Ackermann's function and inverse:}
\begin{DisplayFormulae}{1}{0pt}{3ex plus 1ex minus 1ex}{\SmallChar}{\StyleWithoutNumber}
{%This equation is just too wide and not easy to split, font size
%reduction seems to be the easiest solution
%\fontsize{9.3pt}{10pt}\selectfont
\fontsize{8.8pt}{9.6pt}\selectfont
\Fm{a(i,j) =
\left\{%
\begin{array}{lr}
2^j &\MathRemark[\relax]{i = 1} \\
a(i-1,2) &\MathRemark[\relax]{j=1} \\
a(i-1,a(i,j-1)) &\MathRemark[\relax]{i,j \geq 2}
\end{array}
\right.%
}
}
%Force the next formula on a new line
\NewParFormulae
\Fm{\alpha(i) = \min\{j \mid a(j,j) \geq i \}}
\end{DisplayFormulae}
}%
}
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