Some Generalizations of Spivey's Bell Number Formula

Some Generalizations of Spivey's Bell Number Formula

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...

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Veröffentlicht in:arXiv.org 2018-03
Hauptverfasser: Mangontarum, Mahid M, Dibagulun, Amerah M
Format: Artikel
Sprache:eng
Schlagworte:
Commutation
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Zusammenfassung: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.
ISSN:2331-8422