# 2D variable coefficient recurrence relation

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.

## Answers and Replies

Science Advisor
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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.

rsq_a
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 realise 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.