Definition:Stirling Numbers of the Second Kind/Complex Numbers
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Definition
Donald E. Knuth, in his The Art of Computer Programming: Volume 1: Fundamental Algorithms, 3rd ed. of $1997$, suggests an extension of the Stirling numbers of the second kind $\ds {r \brace r - m}$ 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.
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Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.6$: Binomial Coefficients