Looking for a recursion relation

[topsquark]

I don't know how to do a search for information on a specific equation. It's \(\displaystyle f(n + 1) = 2 - \dfrac{d(n)}{f(n)}\), where d(n) is more or less arbitrary. It came up in some work I've been doing and I can't seem to get anywhere with it. Being non-linear it may not even have a closed form solution. There are two other ways to look at it. It's a non-linear difference equation: \(\displaystyle f \Delta f + f(f - 2) = d\) and it can also be considered as a continued fraction. (I'm going to be looking up that idea tonight.)

Any thoughts?

-Dan

 

[pbuk]

Any thoughts?

Yes, I think that it is impossible to make any general conclusions as the answer depends completey on $d(n)$.

 

[topsquark]

Yes, thank you. I have found (but not proven) that this equation cannot be solved in general. I haven't even found a general way to approach it. It is a very annoying little equation!

-Dan

Addendum: Well, I should say "does not have closed form solutions in general." We can always do it numerically.