Regular Article: A Unified Approach to Generalized Stirling Numbers

Authors:
Leetsch C. Hsu;Peter Jau-Shyong Shiue
Affiliations:
Institute of Mathematics, Dalian University of Technology, Dalian, 116024, China;Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, Nevada, 89154-4020
Venue:
Advances in Applied Mathematics
Year:
1998

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Abstract

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.