# Definition:Stirling Numbers/Historical Note

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## Historical Note on Stirling Numbers

This formula for the Stirling numbers of the second kind:

- $\displaystyle x^n = \sum_k {n \brace k} x^{\underline k}$

was the reason James Stirling started his studies of the Stirling numbers in the first place.

They were studied in detail in his *Methodus Differentialis* of $1730$.

## Sources

- 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.6$: Binomial Coefficients: $(45)$