A \(q\)-analogue of \(r\)-Whitney numbers of the second kind and its Hankel transform
Volume 21, Issue 3, pp 258--272
http://dx.doi.org/10.22436/jmcs.021.03.08
Publication Date: April 29, 2020
Submission Date: January 28, 2020
Revision Date: February 21, 2020
Accteptance Date: March 18, 2020
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Authors
Roberto B. Corcino
- Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmeña Boulevard, Cebu City, Philippines.
Jay M. Ontolan
- Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmeña Boulevard, Cebu City, Philippines.
Jennifer Cañete
- Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmeña Boulevard, Cebu City, Philippines.
Mary Joy R. Latayada
- Mathematics Department, Caraga State University, Butuan City, Philippines.
Abstract
A \(q\)-analogue of \(r\)-Whitney numbers of the second kind, denoted by \(W_{m,r}[n,k]_q\), is defined by means of a triangular recurrence relation. In this paper, several fundamental properties for the said \(q\)-analogue are established including other forms of recurrence relations, explicit formulas and generating functions. Moreover, a kind of Hankel transform for \(W_{m,r}[n,k]_q\) is obtained.
Share and Cite
ISRP Style
Roberto B. Corcino, Jay M. Ontolan, Jennifer Cañete, Mary Joy R. Latayada, A \(q\)-analogue of \(r\)-Whitney numbers of the second kind and its Hankel transform, Journal of Mathematics and Computer Science, 21 (2020), no. 3, 258--272
AMA Style
Corcino Roberto B., Ontolan Jay M., Cañete Jennifer, Latayada Mary Joy R., A \(q\)-analogue of \(r\)-Whitney numbers of the second kind and its Hankel transform. J Math Comput SCI-JM. (2020); 21(3):258--272
Chicago/Turabian Style
Corcino, Roberto B., Ontolan, Jay M., Cañete, Jennifer, Latayada, Mary Joy R.. "A \(q\)-analogue of \(r\)-Whitney numbers of the second kind and its Hankel transform." Journal of Mathematics and Computer Science, 21, no. 3 (2020): 258--272
Keywords
- \(r\)-Whitney numbers
- \(r\)-Dowling numbers
- generating function
- \(q\)-exponential function
- symmetric function
- Hankel transform
MSC
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