small o notation

Hi! I'm writing a dissertation on the Number Field Sieve and I just can't get my head around small o notation. It's so embarrassing!! If anyone could help me justify this step in my calculations, I would be so grateful!!

(1+o(1))2(lnn)^{1/3}(ln2+1/3ln{lnn})^{2/3} ~(1+o(1))2(lnn)^{1/3}(1/9)^{1/3}(lnlnn)^{2/3}

Basically, just where the ln2 goes.

Thanks in advance!

Emma.

I assume f(n) ~ g(n) here means that f(n) / g(n) → 1 when n → ∞. If f(n) → ∞ and c, a are constants, then (c + f(n))^a ~ (f(n))^a. Just factor out (f(n))^a.

Thank you so much! It has nothing to do with the small-o!