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Homework Statement
Use Sterling's approximation to show that the multiplicity of an Einstein solid, for any large values of N and q is approximately
[tex]\Omega(N,q) = \frac{(\frac{q+N}{q})^q(\frac{q+N}{N})^N}{\sqrt{2\pi q(q+N)/N}}[/tex]
Homework Equations
[tex]\Omega(N,q) = \frac{(N+q-1)!}{q!(N-1)!}[/tex]
[tex]\ln(x!) \simeq x\ln(x) - x[/tex]
The Attempt at a Solution
I see where the terms in the numerator come from, but I cannot see where the terms in the denominator come from. Specifically, the squareroot, and the factor of 2 pi*q. When I grind out the math, I get that the denominator should be (q+N)/N. Help anyone?
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