May 2011
Beginner
492 pages
14h 16m
English
Content preview from Heat and Thermodynamics
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13.3 Stirling's Theorem
The value of n! increases very quickly with n. 30! produces a member requiring 33 figures to write. Stirling gave an approximate formula for n!
Taking log of both sides,
It can be proved in the following way
ln n! = ln1 + ln2 + ln3 + … + ln x + … + ln n
ln nn = ln n + ln n + ln n + … + ln n + … + ln n
or
The summation can be approximately replaced by the integration
or
or
ln n
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