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

Volume 24, Issue 3, pp 273--286 http://dx.doi.org/10.22436/jmcs.024.03.08

Publication Date: March 25, 2021 Submission Date: January 16, 2021 Revision Date: January 31, 2021 Accteptance Date: February 24, 2021

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Authors

Roberto B. Corcino - Research Institute for Computational Mathematics and Physics, Cebu Normal University, Cebu City 6000, Philippines. Mary Ann Ritzell P. Vega - Department of Mathematics, Mindanao State University, Iligan Institute of Technology, Iligan City 9200, Philippines. Amerah M. Dibagulun - Department of Mathematics, Mindanao State University, Main Campus, Marawi City 9700, Philippines.

Abstract

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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Keywords

• \(r\)-Whitney numbers
• \(r\)-Whitney-Lah numbers
• \(r\)-Dowling numbers
• generating function
• Qi-type formula

MSC

•  05A19
•  05A30
•  11B65

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