Correction to the first printing of third edition: The exponent in the result should be \(-3 / 2\). For \(\beta m c^{2} \gg 1\) but before the time when the electron density approaches the protron density, the density of electrons and positrons are almost identical so \(\mu \approx 0\). Equation (9.5.6) gives

\[
\begin{aligned}
\frac{n_{-}}{n_{\gamma}} \approx \frac{n_{+}}{n_{\gamma}} & \approx \frac{1}{\zeta(3)} \int_{\beta m c^{2}}^{\infty} \frac{x \sqrt{x+\beta m c^{2}} \sqrt{x-\beta m c^{2}} d x}{e^{x}+1} \\
& \approx \frac{e^{-\beta m c^{2}}\left(\beta m c^{2} \right)^{3 / 2}}{2 \zeta(3)} \int_{0}^{\infty} \sqrt{y} e^{-y} d y
\end{aligned}
\]