Show that for an ideal Bose gas [ langle uangleleftlanglefrac{1}{u}ightangle=frac{4}{pi} frac{g_{1}(z) g_{2}(z)}{left{g_{3 / 2}(z)ight}^{2}} ] (u) being

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Show that for an ideal Bose gas

\[
\langle uangle\left\langle\frac{1}{u}ightangle=\frac{4}{\pi} \frac{g_{1}(z) g_{2}(z)}{\left\{g_{3 / 2}(z)ight\}^{2}}
\]

\(u\) being the speed of a particle. Examine and interpret the limiting cases \(z ightarrow 0\) and \(z ightarrow 1\); compare with Problem 6.6.

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