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Quick math question

  1. Sep 19, 2005 #1
    How does the following expand;

    (q + N )*ln(q +N)

    I'm Trying to arrive at sterling approximation for the multiplicity for einstein solid where q>>N. Any tips appreciated.

  2. jcsd
  3. Sep 19, 2005 #2
    factor out the bigger of the two

    [tex] q(1 + \frac{N}{q} \ln q(1 + \frac{N}{q}) [/tex]

    i gues you could 'expand it using the log expansion
    [tex] ln (1+x) = x - \frac{1}{2} x^2 + \frac{1}{3} x^3 - ... [/tex]
  4. Sep 20, 2005 #3

    I'm going to have to see my prof. on this one. I'll let you know how it works out if you'd like.
  5. Sep 20, 2005 #4


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    I guess N stands for the number of particles (phonons), so it should be the "bigger" one. I also think that Stirling's approximation involves factorials.

  6. Sep 20, 2005 #5
    For my next exercise I'm to derive the case where N >> q. In these simple idealized cases of 2 solids interacting. So big q is high temp case- I think.
    I've already used the sterling approximation to get the factorials out of the equation and now I'm just hashing it into best form.

    many thanks.
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