%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}
   }%
}
