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A Unified Approach to Generalized Stirling Numbers

✍ Scribed by Leetsch C. Hsu; Peter Jau-Shyong Shiue

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
191 KB
Volume
20
Category
Article
ISSN
0196-8858

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that various well-known generalizations of Stirling numbers of the first and second kinds can be unified by starting with transformations between generalized factorials involving three arbitrary parameters. Previous extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Tsylova, and others are included as particular cases of our unified treatment. We have also investigated some basic properties related to our general pattern.

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