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

Definition
, in his 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.