New in Wolfram Mathematica 7: Enhanced Fourier Analysis  previous | next 
Generate Symbolic Fourier Coefficients
Fourier coefficient gallery.
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problems = {HoldForm[FourierCoefficient[1, t, n]], 

   HoldForm[FourierCoefficient[E^(I t), t, n]], 

   HoldForm[FourierCoefficient[SquareWave[x/(2 \[Pi])], x, n]], 

   HoldForm[FourierCoefficient[TriangleWave[x/(2 \[Pi])], x, n]], 

   HoldForm[FourierCoefficient[SawtoothWave[x/\[Pi]], x, n]], 

   HoldForm[FourierCoefficient[Abs[t], t, n]]};
In[2]:=

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FormulaGallery[forms_List] := 

  Module[{vals = ParallelMap[ReleaseHold, forms]}, 

   Text[TraditionalForm[

     Grid[Table[{forms[[i]], "==", vals[[i]]}, {i, Length[forms]}], 

      Dividers -> {{True, False, False, True}, All}, 

      Alignment -> {{Right, Center, Left}, Baseline}, 

      Background -> LightYellow, Spacings -> {3, 3}]]]];
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FormulaGallery[problems]
Out[3]=