Closed-Form Solution for f(n) w/o Generating Fns

[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.

 

[dextercioby]

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

Daniel.

 

[HallsofIvy]

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

 

[Tony11235]

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

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.

 

[Tony11235]

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