The average particle energy of a Fermi-Dirac gas, with zero chemical potential, is about 3.15T, where T is the temperture of this gas. To get the average energy, one needs to do an integration. The integrand is something like(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{x^3}{e^{x/k_BT}+1}[/itex].

I could get the result numerically. But is there a way to do it analytically? Thanks.

[updated] Sorry. The expression is corrected now. So basically I would like to know whether the following can be integrated analytically:

[itex]\int_0^\infty \frac{x^3}{e^{x/k_BT}+1} dx [/itex]

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# Is there an analytical way to get average energy of a Fermi-Dirac gas?

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