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M. Aigner, A Characterization of the Bell Numbers, Discrete Math. 205 (1999), 207-210.

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Article

On Noncentral Bell Numbers and Their Hankel Transforms

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


Turkish Journal of Analysis and Number Theory. 2014, Vol. 2 No. 2, 29-36
DOI: 10.12691/tjant-2-2-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Roberto B. Corcino, Harren Jaylo-Campos, 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.

Correspondence to: Roberto  B. Corcino, Department of Mathematics, Mindanao State University, Marawi City, Philippines. Email: rcorcino@yahoo.com

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.

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