Question

Big O notation: How to simplify this:
\[\left(1+ \frac{1}{4n}+O\left(\frac{1}{n^2}\right)\right)^2\]

Sorry I am not too familiar with using big O notation.

Answer 1

me too, that looks new for me :v

Answer 2

if anyone needs more information, I encountered this as coming from the following result, which is a ratio of 2 gamma functions:

\[\frac{\Gamma (k+a)}{\Gamma (k+b)} = k^{a-b} \left[ 1+ \frac{(a+b-1)(a-b)}{2k}+O\left(\frac{1}{k^2}\right)\right], \text{for sufficiently large }k \]