Solve New Classes of Functional Equations
Solve new classes of functional equations, including arithmetic geometric, linear fractional and geometric power.
 In:= ```problems = {{"Arithmetic", HoldForm[ RSolve[y[n + 1/3] == 2 y[n + 1/6] + n^2, y[n], n]]}, {"Geometric", HoldForm[ RSolve[y[n] == -2 y[n/2] + y[n/4] + n, y[n], n]]}, {"Arithmetic geometric", HoldForm[ RSolve[y[n] == 2^(n/2) y[n/2 + 1] + 9 2^n (n/2 + 1), y[n], n]]}, {"Linear fractional", HoldForm[RSolve[y[(2 n - 1)/(-n + 2)] == 3 y[n] + 5, y[n], n]]}, {"Geometric power", HoldForm[RSolve[ y[n] == Sqrt[n] y[Sqrt[n]] + n, y[n], n ]]}, {"General", HoldForm[RSolve[y[Exp[n]] == -2 y[Exp[n/2]] + n, y[n], n]]}};```
 In:= ```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 -> {Automatic, 2}]]```
 In:= `FormulaGallery[Last /@ problems]`
 Out=  