The translated Whitney–Lah numbers: generalizations and q-analogues

Mangontarum, Mahid M.

doi:10.7546/nntdm.2020.26.4.80-92

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This Is Exactly Equation (33)1

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2021

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“…Applying the exponential generating function of the (p, q)-analogue of r-Whitney numbers of the second kind in Remark 2.6 yields the desired exponential generating function in (4.3). Now, Qi [24] obtained an explicit formula for the Bell numbers expressed in terms of both the Lah numbers and the Stirling numbers of the second kind by Other similar works can be seen in [5,20].…”

Section: This Is Exactly Equation (33)mentioning

confidence: 99%

A ( p,q )-analogue of Qi-type formula for r -Dowling numbers

Corcino¹,

Vega²,

Dibagulun³

2021

J. Math. Computer Sci.

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In this paper, (p, q)-analogues of r-Whitney numbers of the first and second kinds are defined using horizontal generating functions. Several fundamental properties such as orthogonality and inverse relations, an explicit formula, and a kind of exponential generating function are obtained. Moreover, a (p, q)-analogue of r-Whitney-Lah numbers is also defined in terms of a horizontal generating function, where necessary properties are obtained. These properties help develop a (p, q)-analogue of the r-Dowling numbers, particularly, a (p, q)-analogue of a Qi-type formula.

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Section: This Is Exactly Equation (33)mentioning

confidence: 99%