1. The problem statement, all variables and given/known data
Show that the multiplicity of an Einstein solid with large N and q is
[tex]\frac{\left(\frac{q+N}{q}\right)^q\left(\frac{q+N}{N}\right)^N}{\sqrt{2 \pi q\left(q+N\right)/N}}[/tex]
2. Relevant equations
[tex]N! \approx N^N e^{N} \sqrt{2 \pi N}[/tex]
3. The attempt at a solution
Well, I've done thus so far:
[tex]
\Omega(N,q) = \frac{(q+N1)!}{q!(N1)!} \approx \frac{(q+N)!}{q!N!}
ln(\Omega) = ln(q+N)!  lnq!  lnN
\par
\approx (q+N)ln(q+N)  (q+N)  qlnq+q  NlnN + N = (q+N)ln(q+N)  qlnq  NlnN
[/tex]
I feel like I'm close, but I've no idea where to go from here.
