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Quick math question

  • Thread starter Barley
  • Start date
  • #1
17
0
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.

Thanks
 

Answers and Replies

  • #2
1,444
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]
 
  • #3
17
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Thanks,

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.
 
  • #4
dextercioby
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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.


Daniel.
 
  • #5
17
0
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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