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Li$_{ν}$( z ), where z = e βµ is a fugacity, using ∫ d $^{d}$k = 2 π d/ $^{2}$/ Γ( d/ 2) ∫ dkk d − 1 and the integrals 

valid for Re( ν ) > 0. The result, as expected, is proportional to T/λ d $_{T}$: 

<img src='content_image/372476.jpg'>

<img src='content_image/372477.jpg'>

There are two important limits to consider. For Bose gases near Bose-Einstein condensation, physically the interesting limit is µ/T → 0. Since Li$_{ν}$(1) = ζ ( ν ), where ζ is Riemann’s zeta function, this leads us to define the scaling functions c$_{d}$ ( µ/T ): 

<img src='content_image/372478.jpg'>

where we have used ζ (2) = π $^{2}$/ 6. With the above normalizations, c$_{d}$ = 1 for a single free boson when µ/T = 0. 

The above formulas are well-defined for fermions at zero chemical potential. Using 

one finds as µ/T → 0: 

<img src='content_image/372480.jpg'>

<img src='content_image/372479.jpg'>

It should be pointed out that the coefficients c$_{d}$ are analogous to the Virasoro central charge for relativistic systems in d = 1, as discussed in [27]. 

The other interesting limit is T/µ → 0, i.e. z → ∞ or z → 0, depending on the sign of the chemical potential. Here the scaling forms are naturally based on the 

