# Handling recurrence relations

Are there special features in Mathematica for probing a recurrence relation? (dummy example: $f(x) = \prod_{i=1}^N f(x-i)$)

Such as, potential simplification, finding base cases, or a visualisation of its iterations.

As an amateur user, any hints would be highly useful.

• Maybe this helps: Table[RSolve[f[x] == Product[f[x - i], {i, 1, n}], f[x], x], {n, 0, 5}] // MatrixForm – Mariusz Iwaniuk Jul 14 '17 at 12:32
• @MariuszIwaniuk ah this is neat. If there are conditions for side-cases, e.g. if x<0, f(x)=0, how do I include them in the RSolve as written by you? – user21766 Jul 14 '17 at 12:51
• You mean Include a boundary condition? – Mariusz Iwaniuk Jul 14 '17 at 13:00
• @MariuszIwaniuk yes it can also be seen as some form of boundary condition. The reason I ask, it is because in the documentation of mathematica we have only examples of the kind RSolve[a[i + 1, j + 1] == i j a[i, j], a[i, j], {i, j}] but what if we wanted to add a condition of the kind a[i,j]=0 if i=j, in the RSolve, an immediate attempt like this RSolve[{a[i + 1, j + 1] == i j a[i, j], a[i,j]=0 if i==j}, a[i, j], {i, j}] doesn't seem to work. – user21766 Jul 14 '17 at 13:13