### Math ClubStirling's FormulaMatt Lamoureux (The Hartford)

Wednesday, February 12, 2020
5:45pm – 6:35pm

Storrs Campus
Monteith 234

The factorials $$n! = 1 \cdot 2 \cdot 3 \cdots n$$, which count how many ways $$n$$ objects can be arranged, show up anywhere that rearrangements have to be counted, such as combinatorics, probability, thermodynamics, statistical mechanics, and quantum mechanics. The numbers $$n!$$ grow very rapidly, e.g., 100! has 158 digits. For applications in chemistry, $$n!$$ may occur for $$n$$ on the order of Avogadro's number (about $$6.02 \times 10^{23}$$), for which an exact calculation is out of the question. When exact values are computationally inaccessible, it's natural to seek approximations to the values.

Stirling's formula is the standard way to estimate $$n!$$ when $$n$$ is large. In this talk we will see what Stirling's formula is and how to derive it using tools from calculus.

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