On Noncentral Bell Numbers and Their Hankel Transforms

Roberto B. Corcino^1, , Harren Jaylo-Campos¹ and Amila P. Macodi-Ringia¹

¹Department of Mathematics, Mindanao State University, Marawi City, Philippines

Cite this paper:
Roberto B. Corcino, Harren Jaylo-Campos and Amila P. Macodi-Ringia. On Noncentral Bell Numbers and Their Hankel Transforms. Turkish Journal of Analysis and Number Theory. 2014; 2(2):29-36. doi: 10.12691/tjant-2-2-1

Abstract

The noncentral Stirling numbers of the first and second kind are certain generalization of the classical Stirling numbers of both kinds. In this paper, a kind of generalized Bell numbers, called noncentral Bell numbers, are defined in terms of noncentral Stirling numbers of the second kind. Some properties parallel to the ordinary Bell numbers are established including the Hankel transform of noncentral Bell numbers. Moreover, an alternative proof for the Hankel transform of (r, β)-Bell numbers is presented.

Keywords:
Stirling numbers Bell numbers Whitney numbers Dowling numbers Catalan numbers binomial transform Hankel transform

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