×

Stirling numbers revisited. (English) Zbl 0951.11009

Summary: The domains of the Stirling numbers of both kinds are extended from \(\mathbb{N}^2\) to \(\mathbb{Z}^2\). These extensions lead to Laurent series, ‘special branches’ and interesting formulas (including the ‘Stirling Duality Law’).

MSC:

11B73 Bell and Stirling numbers
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abramowitz, M.; Stegun, I.A., ()
[2] Berge, C., Principles of combinatories, (1971), Academic Press New York · Zbl 0227.05002
[3] Cohen, D.I.A., Combinatorial theory, (1978), Wiley New York
[4] Comtet, L., Advanced combinatorics, (1974), Reidel Boston
[5] Gessel, I.; Stanley, R.P., Stirling polynomials, J. comb. theory (A), 28, 24-33, (1978) · Zbl 0378.05006
[6] Gould, H.W., The q-Stirling numbers of the first and second kinds, Duke math. J., 28, 281-289, (1961) · Zbl 0201.33601
[7] Graham, R.L.; Knuth, D.E.; Patashnik, O., Concrete mathematics, (1989), Addison-Wesley Reading, MA · Zbl 0668.00003
[8] Jordan, C., On Stirling’s numbers, Tohoku math. J., 37, 254-278, (1933) · JFM 59.0171.01
[9] Knuth, D.E., Two notes on notation, Amer. math. monthly, 99, 403-422, (1992) · Zbl 0785.05014
[10] Krouse, D.P.; Olive, G., Binomial functions with the Stirling property, J. math. anal. appl., 83, 110-126, (1981) · Zbl 0477.05004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.