Sample Symbolic Discrete Ratios
Sample some formulas for symbolic discrete ratios.
 In[1]:= ```problems = {HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)]\(f[k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)]\( \*SubscriptBox[\(\[Product]\), \(k\)]f[k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)] \*SuperscriptBox[\(a\), \(k\)]\)], HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)]\(( \*FractionBox[\( \*SuperscriptBox[\(k\), \(2\)] + 1\), \(k^3 + 1\)])\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)]\(( \*FractionBox[\(Pochhammer[ \*SubscriptBox[\(a\), \(1\)], k] Pochhammer[ \*SubscriptBox[\(a\), \(2\)], k]\), \(Pochhammer[ \*SubscriptBox[\(b\), \(1\)], k] Pochhammer[ \*SubscriptBox[\(b\), \(2\)], k]\)])\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)]\(CatalanNumber[k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)]\(BarnesG[k]\)\)], HoldForm[\!\( \*SubscriptBox[\(\[DiscreteRatio]\), \(k\)]\(QFactorial[k, q]\)\)]};```
 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]=