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+%This command provides the text for the hyperbolic function in
+%the second part of the second column in page 4
+%
+%This macro has one parameter
+% 1) The width allowed to typeset the text
+\newcommand\TFourHyperbolic[1]{%
+ \parbox[t]{#1}{%
+ \DisplaySpace{\TFourDisplaySpace}{\TFourDisplayShortSpace}
+
+ \TFourTitle{Definitions:}
+ \begin{DisplayFormulae}{1}{0pt}{\TFourSkipFormulae}{\BigChar}{\StyleWithoutNumber}
+ \def\LineOfArray##1##2##3##4{\rule{0pt}{4ex plus .5ex minus 1ex}%
+ {##1}&=&{##2}&{##3}&=&{##4}\\}
+ \Fm{\begin{array}{l%Equal sign
+ @{\hspace{.1em}}c@{\hspace{.2em}}%
+ l%
+ l%
+ @{\hspace{.1em}}c@{\hspace{.2em}}%
+ l}
+ \LineOfArray{\sinh x}{\frac{e^x - e^{-x}}{2}}%
+ {\cosh x}{\frac{e^x + e^{-x}}{2}}
+ \LineOfArray{\tanh x}{\frac{e^x - e^{-x}}{e^x + e^{-x}}}
+ {\csch x}{\frac{1}{\sinh x}}
+ \LineOfArray{\sech x}{\frac{1}{\cosh x}}
+ {\coth x}{\frac{1}{\tanh x}}
+ \end{array}%
+ }
+ \end{DisplayFormulae}
+
+ \TFourTitle{Identities:}
+ \AdjustSpace{1ex plus .5ex minus .5ex}
+ \begin{DisplayFormulae}{1}{0pt}{\TFourSkipFormulae}{\BigChar}{\StyleWithoutNumber}
+ \def\FmSep{\unskip\text{,}}%use a comma as separator for the formula
+ \Fm{\cosh^2 x - \sinh^2 x = 1}
+ \Fm{\tanh^2 x + \sech^2 x = 1}
+ \Fm{\coth^2 x - \csch^2 x = 1}
+ \Fm{\sinh (-x) = - \sinh x}
+ \Fm{\cosh (-x) = \cosh x}
+ \Fm{\tanh (-x) = - \tanh x}
+ \Fm{\sinh (x + y) = \sinh x \cosh y + \cosh x \sinh y}
+ \Fm{\cosh (x + y) = \cosh x \cosh y + \sinh x \sinh y}
+ \Fm{\sinh 2x = 2 \sinh x \cosh x}
+ \Fm{\cosh 2x = \cosh^2 x + \sinh^2 x}
+ \Fm{\cosh x + \sinh x = e^x}
+ \Fm{\cosh x - \sinh x = e^{-x}}
+ \def\FirstPart{(\cosh x + \sinh x)^n = \mbox{}}
+ \FmPartA{\FirstPart\cosh n x +}
+ \FmPartB{\FirstPart}{\sinh n x \MathRemark{n \in \Z}}
+ \Fm{2 \sinh^2 \tfrac{x}{2} = \cosh x - 1}
+ \def\FmSep{\unskip\text{.}}
+ \Fm{2 \cosh^2 \tfrac{x}{2} = \cosh x + 1}
+ \end{DisplayFormulae}
+ }
+}