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{\bf TABLE OF FOURIER TRANSFORMS}
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The functions in the table are defined for  $-\pi<x<\pi\/$.

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\begin{tabular}{l|l}
{\em function}&
   {\em Fourier series}\\ \hline
\            & \   \\
$x\/$        &               $2\sum _{n=1}^\infty \frac {(-1)^ {n+1}}n 
                            \sin nx\/$\\
\            &  \ \\


$|x|\/$      &               $ \frac \pi 2 - \frac 2\pi \sum _{n=1}^\infty
                            \frac  {1-(-1)^n} {n^2} \cos nx\/$\\
\            & \    \\

$x^2\/$      &               $\frac{\pi^2}3 +4 \sum_{n=1}^\infty 
                            \frac{(-1)^n}{n^2}\cos nx\/$\\
\            &  \  \\

$x^3\/$      &               $2\sum_{n=1}^\infty(-1)^n\left(
                            \frac 6 {n^3 } -\frac   {\pi^2}{n}\right)
                             \sin nx\/$\\
\            &  \ \\
$f(x)\/$     &              $ \sum _{n=1}^\infty \frac 2{n\pi} 
                               \left(1-(-1)^n\right) \sin n\pi\/$	
\end{tabular}

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The function  $f\/$
in the table is  equal to $1\/$ if  $0<x<\pi\/$
and  $-1\/$
if  $-\pi < x < 0\/$.

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