# Closed form

1. Oct 3, 2006

### Tony11235

$$f(n) = 0, n \leq 2$$

$$f(n) = \sqrt{n}f(\sqrt{n}) + n, n > 2$$

How can I get this in closed form? Generating functions won't work. Recuring a number of times hasn't worked out for me. Or can I show that f = O(n*lg(lg(n))), where lg stands for ln(n)/ln(2), without f being in closed form? Sorry for the poor tex skills.

Last edited: Oct 4, 2006
2. Oct 4, 2006

### dextercioby

I don't think it can be put in closed form.

Daniel.

3. Oct 4, 2006

### HallsofIvy

Staff Emeritus
f(n)= kn for $2^{k}< n \le 2^{k+1}$

4. Oct 4, 2006

### Tony11235

Are you serious? This is the closed form I've been struggling all day to find? Could you mention how you arrived at this? Sorry it's not totally obvious to me, I'm really tired.

5. Oct 4, 2006

### Tony11235

Nevermind. No explanation needed. I'm just really pissed with myself.