Ken McLaughlin (Royal Society Wolfson Professor)

Ancient and modern approaches to the asymptotic analysis of integrals of the form $e^{-n\phi(s)} ds$, using the example of Stirling’s formula

Stirling’s formula is the leading asymptotic behavior of $n!$. That’s right, the product of the first $n$ integers and it goes like this:
n! ~ n^{n} e^{-n} \sqrt{2 \pi n } We will see how to derive not only the leading behavior, but also the corrections, using classical techniques – we may not even need Aristotle’s lever! Then we will revisit the derivation, revisiting ideas presented earlier in the semester by Professor Alexander Its.