New in Wolfram Mathematica 7: New Number Theory Capabilities  previous | next 
Evaluate Ordinary and Exponential Generating Functions
In[1]:=

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problems = {HoldForm[GeneratingFunction[ChebyshevU[n, a], n, z]], 

   HoldForm[GeneratingFunction[Mod[n, 7], n, z]], 

   HoldForm[GeneratingFunction[f[n + 1], n, z]], 

   HoldForm[GeneratingFunction[Binomial[m, n], {m, n}, {u, v}]], 

   HoldForm[ExponentialGeneratingFunction[BernoulliB[n], n, z]], 

   HoldForm[ExponentialGeneratingFunction[n^2 + 2, n, z]], 

   HoldForm[ExponentialGeneratingFunction[Sin[a n], n, z]],

   HoldForm[

    ExponentialGeneratingFunction[m/(n + 1), {m, n}, {u, v}]]};
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 -> {1, 2}]];
In[3]:=

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FormulaGallery[problems]
Out[3]=