Compute Symbolic Differences
Compute symbolic differences of sequences.
 In[1]:= ```problems = {HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \(k\)]\(f[k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \(k\)]\( \*SubscriptBox[\(\[Sum]\), \(k\)]f[k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \(k\)] \*SuperscriptBox[\(2\), \(k\)]\)], HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \(k\)]\(PolyGamma[k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \(k\)]\(k!\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \({k, 5}\)]\(Sin[a\ k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \({k, 13}\)]\(Fibonacci[ k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DifferenceDelta]\), \({k, 3}\)]\(BesselJ[k, x]\)\)]};```
 In[2]:= ```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 -> {{4, {}, 4}, 2}]]```
 In[3]:= `FormulaGallery[problems]`
 Out[3]=