and 
Being Held Fixed
We comment on the mathematical significance of setting and constant for the purposes of the derivation. First, note that:
and similarly:
Recall that the density of states 
is defined so
that we can approximate a sum weighted by 
with an integral weighted by
; that is:
We see this formally by noting that 
represents ``the
number of states at energy levels close to E'':
Therefore, we obtain:
Hence, we can view as deriving 
holding and fixed as necessary so that we can recover these values from the
integrals above.
