The bias correction is:
$$g = d_{c} = d_{obs} \times J$$
where
$$J = \frac{\Gamma(\frac{n - 2}{2})}{\sqrt{\frac{n - 2}{2}} \times \Gamma(\frac{n - 3}{2})}$$
and \(d_{obs}\) is the observed effect size, \(g = d_{c}\) is the
corrected (unbiased) estimate, \(n\) is the total sample size, and
\(\Gamma()\) is the gamma function.
Historically, using the gamma function was computationally intensive, so an
approximation for \(J\) was used (Borenstein et al., 2009):
$$J = 1 - 3 / (4 * (n - 2) - 1)$$
This approximation is no longer necessary with modern computers.