Some Generalizations of Spivey's Bell Number Formula

Some Generalizations of Spivey's Bell Number Formula

Matimyas Matematika, Vol. 40 No.1 (2017) pp. 1-12 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 generaliz...

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Hauptverfasser: Mangontarum, Mahid M, Dibagulun, Amerah M
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
Mathematics - Number Theory
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Zusammenfassung:Matimyas Matematika, Vol. 40 No.1 (2017) pp. 1-12 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.
DOI:10.48550/arxiv.1712.09341