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arXiv · 1712.09341

Some Generalizations of Spivey's Bell Number Formula

Mahid M. Mangontarum·Amerah M. Dibagulun
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Abstract

In this paper, a generalized recurrence relation for the $r$-Whitney numbers of the second kind is derived using as framework the operators $X$ and $D$ satisfying the commutation relation $DX-XD=1$. This recurrence relation is shown to be a generalization of the well-known Spivey's Bell number. Moreover, several other identities generalizing Spivey's Bell number formula are obtained.

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Mahid M. Mangontarum, Amerah M. Dibagulun. 2018-03-03. Some Generalizations of Spivey's Bell Number Formula. https://arxiv.org/abs/1712.09341

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