On 10/27/11 2:46 AM, Aleksas Domarkas wrote:
>
> How solve recurence equation d(n)=n*d(n-1)-d(n-2) ?
One technique is to use Z-transforms, a discrete analogue for Laplace
transforms.
Basically for a sequence d(n), n >= 0, the z-transform is D(z) =
sum(d(n)/z^n,n,0,inf). The wikipedia entry for z-transforms contains
some properties of z-transforms that will be useful. In particular
d(n-k) is z^(-k)*D(z) and n*d(n) is -z*diff(D(z),z).
If I did the math right, you end up with D(z) = z*exp(1/z-z). This
looks related to the generating function for Bessel J. Unfortunately,
it doesn't seem like you end up with the Bessel expression you gave, so
I've probably made a mistake.
Ray