Apply q-Functions in Discrete Calculus
Mathematica 7 makes extensive use of q-functions in all discrete calculus operations.
 In[1]:= ```problems = {HoldForm[\!\(TraditionalForm\`\* TemplateBox[{TemplateBox[{"k", "q"}, "QGamma"],"k"}, "DifferenceDelta2"]\)], HoldForm[\!\(TraditionalForm\`\* TemplateBox[{TemplateBox[{"k", "n", "q"}, "QBinomial"],"k"}, "DiscreteRatio2"]\)], HoldForm[\!\(TraditionalForm\` \*UnderoverscriptBox[\(\[Product]\), \(k = 0\), \(n - 1\)]\((1 - a\ \*SuperscriptBox[\(q\), \(k\)])\)\)], HoldForm[\!\(TraditionalForm\` \*UnderscriptBox[\(\[Product]\), \(k\)]sinh(k + 1)\)], HoldForm[\!\(TraditionalForm\` \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\[Infinity]\)] \*FractionBox[\(1\), \( \*SuperscriptBox[\(2\), \(k\)] + 1\)]\)], HoldForm[\!\(TraditionalForm\` \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\[Infinity]\)]\* FractionBox[ RowBox[{ SuperscriptBox["z", "k"], " ", TemplateBox[{"a","q","k"}, "QPochhammer"], " ", TemplateBox[{"b","q","k"}, "QPochhammer"]}], RowBox[{ TemplateBox[{"q","q","k"}, "QPochhammer"], " ", TemplateBox[{"c","q","k"}, "QPochhammer"]}]]\)]};```
 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}, 1}]]```
 In[3]:= `FormulaGallery[problems]`
 Out[3]=