A way of approximating large factorials is through the use of Stirling's Formula: a complete derivation of
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a complete derivation of which is difficult. Instead, prove the easier fact,
and hence
Now compare log n! to the average of the two integrals. See Exercise 5.35 for another derivation.)
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n! lim no nn+(/2a constant. n! lim n00 nn+(/ constant k+1 / rk log z dz
n! lim no nn+(/2a constant. n! lim n00 nn+(/ constant k+1 / rk log z dz
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The average of the two integrals is n log n n n 1 log n 1 n 2 n log n n 1 log n 1 2 n n 12 ...View the full answer
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