Events
DMS Applied Mathematics Seminar |
| Time: Apr 06, 2018 (02:00 PM) |
| Location: Parker Hall 328 |
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Details: Speaker: Prof. Tian-Xiao He, Department of Mathematics at Illinois Wesleyan University. Title: Generalization of Stirling Numbers and Stirling Functions Abstract: Here we present a unified approach to Stirling numbers and their generalizations, as well as generalized Stirling functions by using generalized factorial functions, k-Gamma functions, and generalized divided difference. Previous well-known extensions of Stirling numbers due to Riordan, Carlitz, Howard, Charalambides-Koutras, Gould-Hopper, Hsu-Shiue, Tsylova Todorov, Ahuja-Enneking, and Stirling functions introduced by Butzer and Hauss, Butzer, Kilbas, Trujilloet, and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations and generating functions are discussed. Three algorithms for calculating the Stirling numbers based on our generalization are also given, which include a comprehensive algorithm using the characterization of Riordan arrays. |