Sample Indefinite and Definite Products
Sample indefinite and definite products.
 In[1]:= ```products = {HoldForm[ \!\(\*UnderscriptBox["\[Product]", "k"]\)(k^2 + 7 k + 12)], HoldForm[ \!\(\*UnderscriptBox["\[Product]", "k"]\)3^k (k^2 + 11)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(n\)] \*FractionBox[\( \*SuperscriptBox[\((k + 1)\), \(3\)]\ \((k + 5)\)\), SuperscriptBox[\(k\), \(2\)]]\)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(n\)]\(( \*SuperscriptBox[\(5\), \(k\)] + \*SuperscriptBox[\(6\), \(k\)])\)\)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(k\), \(n\)] \*FractionBox[\(\(( \*SuperscriptBox[\(3\), \(7\ k + 7\)] + 11)\)\(\ \)\), \(\(\ \)\(( \*SuperscriptBox[\(3\), \(2\ k\)] + \*SuperscriptBox[\(3\), \(k\)] + 2)\)\)]\)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(n\)] \*SuperscriptBox[\(( \*FractionBox[\(k + 3\), \(k + 1\)])\), \(k\)]\)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(n\)] \*FractionBox[\(Sin[3\ k + 5]\), \(Cos[3\ k + 1]\)]\)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(k = 1\), \(\[Infinity]\)]\((1 + \*FractionBox[\(1\), SuperscriptBox[\(k\), \(2\)]])\)\)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(k = 0\), \(\[Infinity]\)]\((1 - a\ \*SuperscriptBox[\(q\), \(k\)])\)\)], HoldForm[\!\( \*UnderoverscriptBox[\(\[Product]\), \(i = 1\), \(\[Infinity]\)]\((1 - \*FractionBox[\(4\ \*SuperscriptBox[\(z\), \(2\)]\), \( \*SuperscriptBox[\(\[Pi]\), \(2\)]\ \*SuperscriptBox[\((2\ i - 1)\), \(2\)]\)])\)\)], HoldForm[ Product[1 + 1/Floor[k^2 (k + 4)/(k + 1)], {k, 1, \[Infinity]}]]};```
 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[products]`
 Out[3]=