# 2D variable coefficient recurrence relation

• rsq_a

#### rsq_a

Consider a 2D variable coefficient linear recurrence relation. An example might be:

$$b_{n,j+1} (j+1)(2n-1)(2n-2) = (2n-2+j)(2n-1+j)b_{n-1,j}$$

which has the solution
$$b_{n,j} = \frac{(2n-1+j)!}{(2n-1)!j!}$$

Is there any algorithm that can be used to derive this result? I have a recurrence relation which is a bit more complex than this one.

Difference relations tend to be UGLY with respect to finding nice, explicit formulae.
The continuous analogue, diff. eqs, tend to be easier to generalize about.

arildno said:
Difference relations tend to be UGLY with respect to finding nice, explicit formulae.
The continuous analogue, diff. eqs, tend to be easier to generalize about.

I realize that. I know that for constant coefficient 2D linear recurrence relations, it seems that Z-Transforms can be applied and are mostly successful. I was wondering whether anybody had seen an analogous technique for non-constant coefficient ones.