# Definition:Stirling Numbers of the First Kind/Unsigned/Complex Numbers

## Definition

Donald E. Knuth, in his *The Art of Computer Programming: Volume 1: Fundamental Algorithms, 3rd ed.* of $1997$, suggests an extension of the **unsigned Stirling numbers of the first kind** $\displaystyle {r \brack r - m}$ to the real and complex numbers.

However, beyond stating that such a number is a polynomial in $r$ of degree $2 m$, and providing a few examples, he goes no further than that, and the details of this extension are unclear.

## Sources

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