By eqns. (8.1.4) and (8.1.5), the temperature \(T_{0}\) is given by

\[
\begin{equation*}
T_{0}=\left(\frac{N}{g V f_{3 / 2}(1)}ight)^{2 / 3}\left(\frac{h^{2}}{2 \pi m k}ight) \tag{1}
\end{equation*}
\]

At the same time, the Fermi temperature \(T_{F}\) is given by, see eqn. (8.1.24),

\[
\begin{equation*}
T_{F} \equiv \frac{\varepsilon_{F}}{k}=\left(\frac{3 N}{4 \pi g V}ight)^{2 / 3} \frac{h^{2}}{2 m k} \tag{2}
\end{equation*}
\]

It follows that

\[
\begin{equation*}
\frac{T_{0}}{T_{F}}=\left(\frac{4 \pi}{3 f_{3 / 2}(1)}ight)^{2 / 3} \frac{1}{\pi} \tag{3}
\end{equation*}
\]

Now, by eqn. (E. 16), \(f_{3 / 2}(1)=\left(1-2^{-1 / 2}ight) \zeta(3 / 2) \simeq 0.765\). Substituting this into (3), we get: \(T_{0} / T_{F} \simeq 0.989\).