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

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.


Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

Roberto B. Corcino, Mary Ann Ritzell P. Vega, Amerah M. Dibagulun, A \((p,q)\)-analogue of Qi-type formula for \(r\)-Dowling numbers, Journal of Mathematics and Computer Science, 24 (2022), no. 3, 273--286

AMA Style

Corcino Roberto B., Vega Mary Ann Ritzell P., Dibagulun Amerah M., A \((p,q)\)-analogue of Qi-type formula for \(r\)-Dowling numbers. J Math Comput SCI-JM. (2022); 24(3):273--286

Chicago/Turabian Style

Corcino, Roberto B., Vega, Mary Ann Ritzell P., Dibagulun, Amerah M.. "A \((p,q)\)-analogue of Qi-type formula for \(r\)-Dowling numbers." Journal of Mathematics and Computer Science, 24, no. 3 (2022): 273--286


Keywords


MSC


References