Asymptotic Expansions and Computation of Generalized Stirling Numbers and Generalized Stirling Functions

Research output: Conference PosterPoster


Here presented is 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, and 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. Some asymptotic expansions for the generalized Stirling functions and generalized Stirling numbers are established. In addition, four algorithms for calculating the Stirling numbers based on our generalization are also given.

Original languageAmerican English
StatePublished - Aug 14 2014
EventInternational Congress of Mathematicians Coex -
Duration: Aug 14 2014 → …


ConferenceInternational Congress of Mathematicians Coex
Period8/14/14 → …


  • Mathematics

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