id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4715	Corcino, Roberto Bagsarsa; Corcino, Cristina B.	On Divisibility Property of Type 2 $(p,q)$-Analogue of $r$-Whitney Numbers of the Second Kind	2023	10	.pdf	application/pdf	3033	189	79	)Wm,r[n, k − 1; t]p,q + [mk + r]p,qp mt−kmq−kr−m(k2)Wm,r[n, k; t]p,q. Applying (6) consequently gives W ∗ m,r[n+ 1, k; t]p,q = W ∗ m,r[n, k − 1; t]p,q + Preliminary Results This section provides a brief discussion on some relations that are necessary in deriving the divisibility property of the type 2 (p, q)-analogue of the r-Whitney numbers of the second kind W ∗ m,r[n, k; t]p,q. Multiplying both sides of the recurrence relation in (5) by q−kr−m(k2) yields q−kr−m(k2)Wm,r[n+ 1, k; t]p,q = q−kr−m(k2)qm(k−1)+rWm,r[n, k − 1; t]p,q + q−kr−m(k2)[mk + r]p,qp mt−kmWm,r[n, k; t]p,q q−kr−m(k2)Wm,r[n+ 1, k; t]p,q = q−(k−1)r−m(k−1 2	cache/ejpam-4715.pdf	txt/ejpam-4715.txt